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AIEEE Home page 2005 AIEEE PAPER - 1 (Physics and chemistry)

 

1) Out of the following pair, which one does not have identical dimensions is
1 )   moment of inertia and moment of a force
2 )   work and torque
3 )   angular momentum and Planck's constant
4 )   impulse and momentum
see the answer    see the solution

 

2) The relation between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is
1 )   2 av3
2 )   2 av2
3 )   - 2 abv2
4 )   2 bv3
see the answer    see the solution

 

3) A car starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then
1 )   S = (1/2) f t2
2 )   S = (1/72) f t2
3 )   S = (1/4) f t
4 )   S = (1/6) f t2
see the answer    see the solution

 

4) A particle is moving eastwards with a velocity of 5 ms-1. In 10 seconds the velocity changes to 5 ms-1 northwards. The average acceleration in this time is
1 )   zero
2 )   (1/)ms-2 towards north-west
3 )   (1/)ms-2 towards north-east
4 )   (1/2)ms-2 towards north
see the answer    see the solution

 

5) A projectile can have the same range R for two angles of projection. If t1 and t2 be the times of flights in the two cases, then the product of the two time of flights is proportional to
1 )   1/R
2 )   R
3 )   R2
4 )   1/R2
see the answer    see the solution

 

6) An angular ring with inner and outer radii R1 and R2 is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F1 / F2 is
1 )   1
2 )   R1 / R2
3 )   R2 / R1
4 )   (R1 / R2)2
see the answer    see the solution

 

7) A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
1 )   μs = 1 - 1/n2
2 )  
3 )   μk = 1 - 1/n2
4 )  
see the answer    see the solution

 

8) The upper half of an inclined plane with inclination Φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
1 )   2 tan Φ
2 )   tan Φ
3 )   2 sin Φ
4 )   2 cos Φ
see the answer    see the solution

 

9) A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
1 )   1.5 cm
2 )   1.0 cm
3 )   3.0 cm
4 )   2.0 cm
see the answer    see the solution

 

10) A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s2. he reaches the ground with a speed of 3 m/s. At what height, did he bail out?
1 )   293 m
2 )   111 m
3 )   91 m
4 )   182 m
see the answer    see the solution

 

11) A particle of mass 0.3 kg is subjected to a force F = -kx with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin?
1 )   5 m/s2
2 )   10 m/s2
3 )   3 m/s2
4 )   15 m/s2
see the answer    see the solution

 

12) The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is

1 )   zero
2 )   ML2/K
3 )   L
4 )   ( KL2 ) / ( 2M )
see the answer    see the solution

 

13) A mass m moves with a velocity v and collides inelastically with another identical mass. After collision the 1st mass moves with velocity v/ in a direction perpendicular to the initial direction of motion. Find the speed of the 2nd mass after collision
1 )   2 V /
2 )   V /
3 )   V
4 )   V
see the answer    see the solution

 

14) A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is
1 )   10 m/s
2 )   10 m/s
3 )   40 m/s
4 )   20 m/s
see the answer    see the solution

 

15) A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration a to keep the block stationary. Then a is equal to

1 )   g
2 )   g tan α
3 )   g / tan α
4 )   g cosec α
see the answer    see the solution

 

16) The moment of inertia of a uniform semicircular disc of mass M and radius r about a lime perpendicular to the plane of the disc through the centre is
1 )   Mr2
2 )   (1/2)Mr2
3 )   (1/4)Mr2
4 )   (2/5)Mr2
see the answer    see the solution

 

17) A body A of mass M while falling vertically downwards under gravity breaks into two parts: a body B of mass 1/3 M and a body C of mass 2/3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards
1 )   body C
2 )   body B
3 )   depends on height of breaking
4 )   does not shift
see the answer    see the solution

 

18) A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

1 )   (4/3) L
2 )   L
3 )   (2/3)L
4 )   (3/2)L
see the answer    see the solution

 

19) The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?
1 )   d = 2h
2 )   d = h
3 )   d = h / 2
4 )   d = 3 h / 2
see the answer    see the solution

 

20) A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take G = 6.67 x 10-11 Nm2/kg2)
1 )   6.67 x 10-9 J
2 )   6.67 x 10-10 J
3 )   13.34 x 10-10 J
4 )   3.33 x 10-10 J
see the answer    see the solution

 

21) A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be
1 )   4 cm
2 )   20 cm
3 )   8 cm
4 )   10 cm
see the answer    see the solution

 

22) If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is
1 )   2 Y / S2
2 )   S / (2Y)
3 )   2 S2 Y
4 )   S2 / (2Y)
see the answer    see the solution

 

23) Average density of the earth
1 )   is directly proportional to g
2 )   is inversely proportionally to g
3 )   does not depend on g
4 )   is a complex function of g
see the answer    see the solution

 

24) A body of mass m is accelerated uniform from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time is given by
1 )   (1/2) . (mv2/T2) . t
2 )   (1/2) . (mv2/T2) . t2
3 )   (mv2/T2) . t
4 )   (mv2/T2) . t2
see the answer    see the solution

 

25) Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped is [μk = 0.5]
1 )   100 m
2 )   400 m
3 )   800 m
4 )   1000 m
see the answer    see the solution

 

26) Which of the following is incorrect regarding the first law of thermodynamics?
1 )   It introduces the concept of the internal energy
2 )   It introduces the concept of the entropy
3 )   It is not applicable to any cyclic process
4 )   It is a restatement of the principle of conservation of energy
see the answer    see the solution

 

27) The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

1 )   1 / 3
2 )   2 / 3
3 )   1 / 2
4 )   1 / 4
see the answer    see the solution

 

28) The figure shows a system of two concentric spheres of radii r1 and r2 and kept at temperature T1 and T2 respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

1 )   r1 r2 / ( r2 - r1 )
2 )   ( r2 - r1 )
3 )   ( r2 - r1 ) / ( r1 r2 )
4 )   ln (r2 / r1)
see the answer    see the solution

 

29) A system goes from A to B via two processes I and II as shown in figure. If ΔU1 and ΔU2 are the changes in internal energies in the process I and II respectively, then

1 )   ΔU2 > ΔU2
2 )   ΔU2 < ΔU2
3 )   ΔU2 = ΔU2
4 )   relation between ΔU1 and ΔU2 can not be determined
see the answer    see the solution

 

30) A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio Cp / Cv of the mixture is
1 )   1.4
2 )   1.54
3 )   1.59
4 )   1.62
see the answer    see the solution

 

31) The intensity of gamma radiation from a given source is I. On passing through 36 mm of lead, it is reduced to I / 8 . . The thickness of lead which will reduce the intensity to I / 2 will be
1 )   18 mm
2 )   12 mm
3 )   6 mm
4 )   9 mm
see the answer    see the solution

 

32) The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The band gap in (eV) for the semiconductor is
1 )   0.5 eV
2 )   0.7 eV
3 )   1.1 eV
4 )   2.5 eV
see the answer    see the solution

 

33) A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 1/2 m away, the number of electrons emitted by photocathode would
1 )   decrease by a factor of 2
2 )   increase by a factor of 2
3 )   decrease by a factor of 4
4 )   increase by a factor of 4
see the answer    see the solution

 

34) Starting with a sample of pure 66Cu, 7/8 of it decays into Zn in 15 minutes. The corresponding halflife is
1 )   5 minutes
2 )   71/2 minutes
3 )   10 minutes
4 )   15 minutes
see the answer    see the solution

 

35) If radius of the nucleus is estimated to be 3.6 Fermi then the radius of nucleus be nearly
1 )   4 fermi
2 )   5 fermi
3 )   6 fermi
4 )   8 fermi
see the answer    see the solution

 

36) The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

1 )   I
2 )   II
3 )   III
4 )   IV
see the answer    see the solution

 

37) If the kinetic energy of a free electron doubles, its deBroglie wavelength changes by the factor
1 )   1/
2 )  
3 )   1/2
4 )   2
see the answer    see the solution

 

38) In a common base amplifier, the phase difference between the input signal voltage and output voltage is
1 )   0 
2 )   π/2
3 )   π/4
4 )   π
see the answer    see the solution

 

39) In a full wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be
1 )   100 Hz
2 )   70.7 Hz
3 )   50 Hz
4 )   25 Hz
see the answer    see the solution

 

40) A nuclear transformation is denoted by X(n, α) . Which of the following is the nucleus of element X?
1 )  
2 )  
3 )  
4 )  
see the answer    see the solution

 

41) The function sin2(ωt) represents
1 )   a simple harmonic motion with a period 2p/ω
2 )   a simple harmonic motion with a period p/ω
3 )   a periodic, but not simple harmonic motion with a period 2p/ω
4 )   a periodic, but not simple harmonic motion with a period p/ω
see the answer    see the solution

 

42) A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is
1 )   straight line
2 )   parabola
3 )   hyperbola
4 )   circle
see the answer    see the solution

 

43) Two simple harmonic motions are represented by the equation y1 = 0.1 sin ( 100 πt + π/3 ) and y2 = 0.1 cos πt . The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is
1 )   - π/3
2 )   π/6
3 )   - π/6
4 )   π/3
see the answer    see the solution

 

44) A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface, the radius of this circle in cm is
1 )   36
2 )   4
3 )   36
4 )   36/
see the answer    see the solution

 

45) Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]
1 )   6 m
2 )   3 m
3 )   5 m
4 )   1 m
see the answer    see the solution

 

46) A thin glass (refractive index 1.5) lens has optical power of 5 D in air. Its optical power in a liquid medium with refractive index 1.6 will be
1 )   25 D
2 )   -25 D
3 )   1 D
4 )   -1 D
see the answer    see the solution

 

47) When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are head. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2?
1 )   196 Hz
2 )   204 Hz
3 )   200 Hz
4 )   202 Hz
see the answer    see the solution

 

48) If a simple harmonic motion is represented by d2x/dt2 + αx = 0 , its time period is
1 )   2πα
2 )   2π
3 )   2π/α
4 )   2π/
see the answer    see the solution

 

49) The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
1 )   remain unchanged
2 )   increase towards a saturation value
3 )   first increase and then decrease to the original value
4 )   first decrease and then increase to the original value
see the answer    see the solution

 

50) An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?
1 )   5 %
2 )   20 %
3 )   zero
4 )   0.5 %
see the answer    see the solution

 

51) If I0 is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?
1 )   I0
2 )   I0/2
3 )   2 I0
4 )   4 I0
see the answer    see the solution

 

52) When an unpolarized light of intensity I0 is incident on a polarizing sheet, the intensity of the light which does not get transmitted is
1 )   zero
2 )   I0
3 )   (1/2) I0
4 )   (1/4) I0
see the answer    see the solution

 

53) A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to
1 )   sin θ
2 )   tan θ
3 )   cos θ
4 )   cot θ
see the answer    see the solution

 

54) Two point charges +8q and -2q are located at x = 0 and x = L respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is
1 )   8 L
2 )   4 L
3 )   2 L
4 )   L / 2
see the answer    see the solution

 

55) Two thin rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and -q. The potential difference between the centres of the two rings is
1 )   zero
2 )  
3 )  
4 )  
see the answer    see the solution

 

56) A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is C then the resultant capacitance is
1 )   C
2 )   nC
3 )   (n - 1)C
4 )   (n + 1)C
see the answer    see the solution

 

57) A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by ΔT, the potential difference V across the capacitance is
1 )   msΔT/C
2 )  
          
3 )  
         
4 )   mCΔT/s
see the answer    see the solution

 

58) One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed V, then the emf induced in the circuit in terms of B, l and V where l is the width of each tube, will be

1 )   zero
2 )   2BlV
3 )   BlV
4 )   - BlV
see the answer    see the solution

 

59) A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be
1 )   one fourth
2 )   halved
3 )   doubled
4 )   four times
see the answer    see the solution

 

60) Two thin, long, parallel wires, separated by a distance d carry a current of i A in the same direction. They will
1 )   attract each other with a force of μ0i2/(2πd2)
2 )   repel each other with a force of μ0i2/(2πd2)
3 )   attract each other with a force of μ0i2/(2πd )
4 )   repel each other with a force of μ0i2/(2πd )
see the answer    see the solution

 

61) A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions per milliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 volt, the resistance in ohms needed to be connected in series with the coil will be
1 )   99995
2 )   9995
3 )   103
4 )   105
see the answer    see the solution

 

62) Two voltameters, one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltammeters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are z1 and z2 respectively the charge which flows through the silver voltameter is
1 )   q . (z1/z2)
2 )   q . (z2/z1)
3 )   ( q )/(1 + (z1/z2) )
4 )   ( q )/(1 + (z2/z1) )
see the answer    see the solution

 

63) In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be

1 )   500 Ω
2 )   1000 Ω
3 )   200 Ω
4 )   100 Ω
see the answer    see the solution

 

64) Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are R1 and R2 (R2 > R1). If the potential difference across the source having internal resistance R2 is zero, then
1 )   R = (R1 . R2) / (R1 + R2)
2 )   R = (R1 . R2) / (R2 - R1)
3 )   R = R2 . ( (R1 + R2)/(R2 - R1) )
4 )   R = R2 - R1
see the answer    see the solution

 

65) Two concentric coils each of radius equal to 2π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the centre of the coils will be (μ0 = 4π x 10-7 Wb/Am)
1 )   5 x 10-5
2 )   7 x 10-5
3 )   12 x 10-5
4 )   10-5
see the answer    see the solution

 

66) A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is
1 )   2πqB / m
2 )   2πm / (qB)
3 )   2πmq / B
4 )   2πq2B / m
see the answer    see the solution

 

67) In a potentiometer experiment the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of 2 Ω , the balancing length becomes 120 cm. The internal resistance of the cell is
1 )   4 Ω
2 )   2 Ω
3 )   1 Ω
4 )   0.5 Ω
see the answer    see the solution

 

68) The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of 100 W and 200 V lamp when not in use?
1 )   400 Ω
2 )   200 Ω
3 )   40 Ω
4 )   20 Ω
see the answer    see the solution

 

69) A magnetic needle is kept in a non-uniform magnetic field. It experiences
1 )   a force and a torque
2 )   a force but not a torque
3 )   a torque but not a force
4 )   neither a force nor a torque
see the answer    see the solution

 

70) A uniform electric field and a uniform magnetic field are acting the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then
1 )   it will turn towards right of direction of motion
2 )   it will turn towards left of direction of motion
3 )   its velocity will decrease
4 )   its velocity will increase
see the answer    see the solution

 

71) A coil of inductance 300 mH and resistance 2 Ω is connected to a sources of voltage 2 V. The current reaches half of its steady state value in
1 )   0.15 s
2 )   0.3 s
3 )   0.05 s
4 )   0.1 s
see the answer    see the solution

 

72) The self inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of
1 )   1 μF
2 )   2 μF
3 )   4 μF
4 )   8 μF
see the answer    see the solution

 

73) An energy source will supply a constant current into the load if its internal resistance is
1 )   zero
2 )   non-zero but less than the resistance of the load
3 )   equal to the resistance of the load
4 )   very large as compared to the load resistance
see the answer    see the solution

 

74) A circuit has a resistance of 12 ohm and an impedance of 15 ohm. The power factor of the circuit will be
1 )   1.25
2 )   0.125
3 )   0.8
4 )   0.4
see the answer    see the solution

 

75) The phase difference between the alternating current and emf is π/2 . Which of the following cannot be the constituent of the circuit?
1 )   L, C
2 )   L along
3 )   C alone
4 )   R, L
see the answer    see the solution

 

76) Which of the following oxides is amphoteric in amphoteric in character ?
1 )   CaO
2 )   CO2
3 )   SiO2
4 )   SnO2
see the answer    see the solution

 

77) Which one of the following species is diamagnetic in nature ?
1 )   He2+
2 )   H2
3 )   H2+
4 )   H2-
see the answer    see the solution

 

78) If α is the degree of dissociation of Na2SO4 the vant Hoff's factor (i) used for calculating the molecular mass is
1 )   1 + α
2 )   1 - α
3 )   1 + 2α
4 )   1 - 2α
see the answer    see the solution

 

79) The oxidation state of Cr in [Cr(NH3)4Cl2]+ is
1 )   + 3
2 )   + 2
3 )   + 1
4 )    0
see the answer    see the solution

 

80) Hydrogen bomb is based on the principle of
1 )   nuclear fission
2 )   natural radioactivity
3 )   nuclear fusion
4 )   artificial radioactivity
see the answer    see the solution

 

81) An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be
1 )   AB
2 )   A2B
3 )   AB3
4 )   A3B
see the answer    see the solution

 

82) For a spontaneous reaction, the ΔG, equilibrium constant (K) and E°cell will be respectively
1 )   -ve, > 1, +ve
2 )   +ve, > 1, -ve
3 )   -ve, <1, -ve
4 )   -ve, >1, -ve
see the answer    see the solution

 

83) Which of the following is a polyamide?
1 )   Teflon
2 )   Nylon-66
3 )   Terylene
4 )   Bakelite
see the answer    see the solution

 

84) Which one of the following types of drugs reduces fever ?
1 )   Analgesic
2 )   Antipyretic
3 )   Antibiotic
4 )   Tranquiliser
see the answer    see the solution

 

85) Due to the presence of an unpaired electron, free radicals are :
1 )   Chemically reactive
2 )   Chemicaly inactive
3 )   Anions
4 )   Cations
see the answer    see the solution

 

86) Lattice energy of an ionic compound depends upon
1 )   Charge on the ion only
2 )   Size of the ion only
3 )   Packing of ions only
4 )   Charge on the ion and size of the ion
see the answer    see the solution

 

87) The highest electrical conductivity of the following aqueous solutions is of
1 )   0.1 M acetic acid
2 )   0.1 M chloroacetic acid
3 )   0.1 M fluoroacetic acid
4 )   0.1 M difluoroacetic acid
see the answer    see the solution

 

88) Aluminium oxide may be electolysed at 1000°C to furnish aluminium metal (at. mass = 27 amu; 1 Faraday = 96,500 Coulombs). The cathode reaction is
Al3+ + 3e- → Al°
To prepare 5.12 kg of aluminium metal by this method would require
1 )   5.49 x 107 C of electricity
2 )   1.83 x 107 C of electricity
3 )   5.49 x 104 C of electricity
4 )   5.49 x 101 C of electricity
see the answer    see the solution

 

89) Consider an endothermic reaction X→Y with the activation energies Eb and Ef for the backward and forward reactions, respectively. In general
1 )   Eb < Ef
2 )   Eb > Ef
3 )   Eb = Ef
4 )   there is no definite relation between Eb and Ef
see the answer    see the solution

 

90) Consider the reaciton : N2 + 3H2 → 2NH3 carried out at constant temperature and pressure. If ΔH and ΔU are the enthalpy and internal energy changes for the reaction, which of the following expressions is true ?
1 )   ΔH = 0
2 )   ΔH = ΔU
3 )   ΔH < ΔU
4 )   ΔH > ΔU
see the answer    see the solution

 

91) Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas ?
1 )   The most probable speed increases
2 )   The fraction of the molecules with the most probable speed increases
3 )   The distribution becomes broader
4 )   The area under the distribution curve remains the same as under the lower temperature
see the answer    see the solution

 

92) The volume of a colloidal particel, Vc as compared to the volume of a solute particle in a true solution Vs, could be
1 )   Vc / Vs ≈ 1
2 )   Vc / Vs ≈ 1023
3 )   Vc / Vs ≈ 10-3
4 )   Vc / Vs ≈ 103
see the answer    see the solution

 

93) The solubility product of a salt having general formula MX2, in water is : 4 x 10-12. The concentration of M2+ ions in the aqueous solution of the salt is
1 )   2.0 x 10-6 M
2 )   1.0 x 10-4 M
3 )   1.6 x 10-4 M
4 )   4.0 x 10-10 M
see the answer    see the solution

 

94) Benzene and toluene form nearly ideal solutions. At 20°C, thevapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at 20°C for a solution containing 78 g of benzene and 46 g of toluene in torr is
1 )   50
2 )   25
3 )   37.5
4 )   53.5
see the answer    see the solution

 

95) The exothermic formation of ClF3 is represented by the equation :

Which of the following will increase the quantity of ClF3 in an equilibrium mixture of Cl2, F2 and ClF3?
1 )   Increasing the temperature
2 )   Removing Cl2
3 )   Increasing the volume of the container
4 )   Adding F2
see the answer    see the solution

 

96) Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 ml of 1.5 M first solution + 520 mL of 1.2 M second solution. What is the molarity of the final mixture ?
1 )   1.20 M
2 )   1.50 M
3 )   1.344 M
4 )   2.70 M
see the answer    see the solution

 

97) For the reaction

(Kc = 1.8 x 10-6 at 184°C)
(R = 0.0831 kJ / (mol.K))
When Kp and Kc are compared at 184°C it is found that
1 )   Kp is greater than Kc
2 )   Kp is less than Kc
3 )   Kp = Kc
4 )   Whether Kp is greater than, less than or equal to Kc depends upon the total gas pressure
see the answer    see the solution

 

98) Hydrogen ion concentration in mol/L in a solution of pH = 5.4 will be :
1 )   3.98 x 108
2 )   3.88 x 106
3 )   3.68 x 10-6
4 )   3.98 x 10-6
see the answer    see the solution

 

99) A reacion involving two different reactants can never be
1 )   unimolecular reaction
2 )   first order reaction
3 )   second order reaction
4 )   bimolecular reaction
see the answer    see the solution

 

100) If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of substance will
1 )   decrease twice
2 )   increase two fold
3 )   remain unchanged
4 )   be a function of the molecular mass of the substance
see the answer    see the solution

 

101) In a multi-electron atom, which of the following orbitals described by the three quantum number will will have the same energy in the absence of magnetic and elctric fields ?
(a) n = 1, l = 0, m = 0
(b) n = 2, l = 0, m = 0
(c) n = 2, l = 1, m = 1
(d) n = 3, l = 2, m = 0
(e) n = 3, l = 2, m = 0
1 )   (a) and (b)
2 )   (b) and (c)
3 )   (c) and (d)
4 )   (d) and (e)
see the answer    see the solution

 

102) During the process of electrolytic refining of copper, some metals present as impurity settle as "anode mud". These are
1 )   Sn and Ag
2 )   Pb and Zn
3 )   Ag and Au
4 )   Fe and Ni
see the answer    see the solution

 

103)
Electrolyte KCl KNO3 HCl NaOAc NaCl
A∞(S cm2 mol-1) 149.9 145.0 426.2 91.0 126.5

Calculate Δ∞HOAc using appropriate molar conductances of the electrolytes listed above at infinite dilution in H2O at 25°C
1 )   517.2
2 )   552.7
3 )   390.7
4 )   217.5
see the answer    see the solution

 

104) A schematic plot of   lnK eq    versus inverse of temperature for a reaction is shown below

The reaction must be
1 )   exothermic
2 )   endothermic
3 )   one with negligible enthalpy change
4 )   highly spontaneous at ordinary temperature
see the answer    see the solution

 

105) The disperse phase in colloidal iron (III) hydroxide and colloidal gold is positively and negatively charged, respectively. Which of the following statements is NOT correct?
1 )   Magnesium chloride solution coagulates, the gold sol more readily than the iron (III) hydroxide sol.
2 )   Sodium sulphate solution causes coagulation in both sols
3 )   Mixing the sols has no effect
4 )   Coagulation in both sols can be brought about by electrophoresis
see the answer    see the solution

 

106) Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point ?
1 )   LiCl
2 )   NaCl
3 )   KCl
4 )   RbCl
see the answer    see the solution

 

107) Heating mixture of Cu2O and Cu2S will give
1 )   Cu + SO2
2 )   Cu + SO3
3 )   CuO + CuS
4 )   Cu2SO3
see the answer    see the solution

 

108) The molecular shapes of SF4, CF4 and XeF4 are
1 )   the same with 2, 0 and 1 lone pairs of electrons
2 )   the same with 1, 1 and 1 lone pair of electrons on the central atoms, respectively
3 )   different with 0, 1 and 2 lone pairs of electrons on the central atom, respectively
4 )   different with 1, 0 and 2 lone pairs of electrons on the central atom, respectively
see the answer    see the solution

 

109) The number and type of bonds between two carbon atoms in calcium carbide are
1 )   One sigma, one pi
2 )   One sigma, two pi
3 )   Two sigma, one pi
4 )   Two sigma, two pi
see the answer    see the solution

 

110) The oxidation state of chromium in the final product formed by the reaction between Kl and acidified potassium dichromate solution is
1 )   +4
2 )   +6
3 )   +2
4 )   +3
see the answer    see the solution

 

111) The number of hydrogen atom(s) attached to phosphorus atom in hypophosphorous acid is
1 )   zero
2 )   two
3 )   one
4 )   three
see the answer    see the solution

 

112) What is the conjugate base of OH- ?
1 )   O2
2 )   H2O
3 )   O-
4 )   O2-
see the answer    see the solution

 

113) The correct order of the thermal stability of hydrogen halides (H-X) is
1 )   HI > HBr > HCl > HF
2 )   HF > HCl > HBr > HI
3 )   HCl < HF > HBr < HI
4 )   HI > HCl < HF > HBr
see the answer    see the solution

 

114) Heating an aqueous solution of aluminium chloride to dryness will give
1 )   AlCl3
2 )   Al2Cl6
3 )   Al2O3
4 )   Al(OH)Cl2
see the answer    see the solution

 

115) Calomel (Hg2Cl2) on reaction with ammonium hydroxide gives
1 )   HgNH2Cl
2 )   NH2-Hg-Hg-Cl
3 )   Hg2O
4 )   HgO
see the answer    see the solution

 

116) In which of the following arrangeements the order is NOT according to the property indicated against it ?
1 )   Al3+ < Mg2+ < Na+ < F- :
Increaing ionic size
2 )   B < C < N < O :
Increasing first ionization enthalpy
3 )   I < Br < F < Cl :
Increasing electron gain enthalpy (with negative sign)
4 )   Li < Na < K < Rb :
Increasing metallic radius
see the answer    see the solution

 

117) In silicon dioxide
1 )   each silicon atom is surrounded by four oxygen atoms and each oxygen atom is bonded to two silicon atoms
2 )   each silicon atom is surrounded by two oxygen atoms and each oxygen atom is bonded to two silicon atoms
3 )   silicon atom is bonded to two oxygen atoms
4 )   there are double bonds between silicon and oxygen atoms
see the answer    see the solution

 

118) Of the following sets which one does NOT contain isoelectronic species ?
1 )   PO43- , SO42- , Cl4-
2 )   CN-, N2, C22-
3 )   BO33- , CO33- , NO3-
4 )   SO32- , CO32- , NO3-
see the answer    see the solution

 

119) The lanthanide contration is responsible for the fact that
1 )   Zr and Y have about the same radius
2 )   Zr and Nb have similar oxidation state
3 )   Zr and Hf have about the same radius
4 )   Zr and Zn have the same oxidation state
see the answer    see the solution

 

120) The IUPAC name of the coordination compound K3[Fe(CN)6] is
2 )   Potassium hexacyanoferrate (II) 1
3 )   Potassium hexacyanoiron (II)
4 )   Tripotassium hexacyanoiron (II)
see the answer    see the solution

 

121) Which of the following compounds shows optical isomerism ?
2 )   [Cu(NH3)2]2+ 1 4]2-
3 )   [Cr(C24O4)3]3-
4 )   [Co(CN)6]3-
see the answer    see the solution

 

122) Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour?
(At. Nos : Cr = 24, Mn = 25, Fe = 26, Co = 27)
2 )   [Cr(CN)6]3- 1 6]3-
3 )   [Fe(CN)6]3-
4 )   [Co(CN)6]3-
see the answer    see the solution

 

123) 2-Methylbutane on reacting with bromine in the presence of sunlight gives mainly
1 )   1-bromo-2-methylbutane
2 )   2-bromo-2-methylbutane
3 )   2-bromo-3-methylbutane
4 )   1-bromo-3-methylbutane
see the answer    see the solution

 

124) A photon of hard gamma radiation knocks a proton out of 1224Mg nucleus to form
1 )   the isotope of parent nucleus
2 )   the isobear of parent nucleus
3 )   the nuclide 1123 Na
4 )   the isobar of 1123 Na
see the answer    see the solution

 

125) The best reagent to convert pent-3-en-2-ol into pent-3-en-2-one is
1 )   Acidic permanganate
2 )   Acidic dichromate
3 )   Chromic anhydride in glacial acetic acid
4 )   Pyridinium chloro-chromate
see the answer    see the solution

 

126) Tertiary alkyl halides are practically inert to substitution by SN2 mechanism because of
1 )   insolubility
2 )   instability
3 )   inductive effect
4 )   steric hindrace
see the answer    see the solution

 

127) In both DNA and RNA, heterocylic base and phosphate ester linkages are at
1 )   C'5 and C'2 respectively of the sugar molecule
2 )   C'2 and C'5 respectively of the sugar molecule
3 )   C'1 and C'5 respectively of the sugar molecule
4 )   C'5 and C'1 respectively of the sugar molecule
see the answer    see the solution

 

128) Reaction of one molecule of HBr with one molecule of 1, 3-butadiene at 40°C gives predominantly
1 )   3-bromobutene under kinetically controlled conditions
2 )   1-bromo-2-butene under thermodynamically controlled conditions
3 )   3-bromobutene under thermodynamically controlled conditions
4 )   1-bromo-2-butene under kinetically controlled conditions
see the answer    see the solution

 

129) Among the following acids which has the lowest pKa value ?
1 )   CH3COOH
2 )   HCOOH
3 )   (CH3)2CH - COOH
4 )   CH3CH2COOH
see the answer    see the solution

 

130) The decreasing order of nucleophilicity among the nucleophiles

1 )   (a), (b), (c), (d)
2 )   (d), (c), (b), (a)
3 )   (b), (c), (a), (d)
4 )   (c), (b), (a), (d)
see the answer    see the solution

 

131) Which one of the following methods is neither meant for the synthesis nor for separation of amines ?
1 )   Hinsberg method
2 )   Hofmann method
3 )   Wurtz reaction
4 )   Curtius reaction
see the answer    see the solution

 

132) Which of the following is fully fluorinated polymer ?
1 )   Neoprene
2 )   Teflon
3 )   Thiokol
4 )   PVC
see the answer    see the solution

 

133) Of the five isomeric hexanes, the isomer which can give two monochlorinated compounds is
1 )   n-hexane
2 )   2, 3-dimethylbutane
3 )   2, 2-dimethylbutane
4 )   2-methylpentane
see the answer    see the solution

 

134) Alkyl halides react with dialkyl copper reagents to give
1 )   alkenes
2 )   alkyl copper halides
3 )   alkanes
4 )   alkenyl halides
see the answer    see the solution

 

135) Acid catalyzed hydration of alkenes except ethene leads to the formation of
1 )   primary alcohol
2 )   secondary or tertiary alcohol
3 )   mixture of primary and secondary alcohols
4 )   mixture of secondary and tertiary alcohols
see the answer    see the solution

 

136) Amongest the following the most basic compound is
1 )   benzylamine
2 )   aniline
3 )   acetanilide
4 )   p-nitroaniline
see the answer    see the solution

 

137) Which types of isomerism is shown by 2, 3-dichlorobutane ?
1 )   Diastereo
2 )   Optical
3 )   Geometric
4 )   Sturctural
see the answer    see the solution

 

138) The reaction

is fastest when X is
1 )   Cl
2 )   NH2
3 )   OC2H5
4 )   OCOR
see the answer    see the solution

 

139) Elimination of bromine from 2-bromobutane results in the formaiton of
1 )   equimolar mixture of 1 and 2-butene
2 )   predominantly 2-butene
3 )   prdominantly 1-butene
4 )   predominantly 2-butyne
see the answer    see the solution

 

140) Equimolar solutions in the same solvent have
1 )   Same boiling point but different freezing point
2 )   Same freezing point but different boiling point
3 )   Same boiling and same freezing points
4 )   Different boiling and different freezing points
see the answer    see the solution

 

141) Which of the following statements in relation to the hydrogen atom is correct ?
1 )   3s orbital is lower in energy than 3p orbital
2 )   3p orbital is lower in energy than 3d orbital
3 )   3s and 3p orbitals are of lower energy than 3d orbital
4 )   3s, 3p and 3d orbitals all have the same energy
see the answer    see the solution

 

142) The structure of diborane (B2H6) contains
1 )   four 2c-2e bonds and two 3c-2e bonds
2 )   two 2c-2e bonds and four 3c-2e bonds
3 )   two 2c-2e bonds and two 3c-3e bonds
4 )   four 2c-2e bonds and four 3c-2e bonds
see the answer    see the solution

 

143) The value of the 'spin only' magnetic moment for one of the following configurations is 2.84 BM. The correct one is
1 )   d4 (in strong ligand field)
2 )   d4 (in weak ligand field)
3 )   d3 (in weak as well as in strong fields)
4 )   d5 (in strong ligand field)
see the answer    see the solution

 

144) Which of the following factors may be regarded as the main cause of lanthanide contraction ?
1 )   Poor shielding of one of 4f electron by another in the subshell
2 )   Effective shielding of one of 4f electrons by another in the subshell
3 )   Poorer shielding of 5d electrons by 4f electrons
4 )   Greater shielding of 5d electron by 4f electrons
see the answer    see the solution

 

145) Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of an acid forms a compound if water during the reaction is continuously removed. The compound formed is generally known as
1 )   a Schiff's base
2 )   an enamine
3 )   an imine
4 )   an amine
see the answer    see the solution

 

146) p-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is
1 )  

2 )  

3 )  

4 )  

see the answer    see the solution

 

147) An organic compound having molecular mass 60 is found to contain C = 20%, H = 6.67% heating it gives NH3 alongwith a solid residue. the solid residue give violet colour with alkaline copper sulphate solution. The compound is
1 )   CH3NCO
2 )   CH3CONH2
3 )   (NH2)2CO
4 )   CH3CH2CONH2
see the answer    see the solution

 

148) If the bond dissociation energies of XY, X2 and Y2 (all diatomic molecules) are in the ratio of 1 : 1 : 0.5 and ΔfH for the formation of XY is -200 kJ mole-1. The bond dissociation energy of X2 will be
1 )   100 kJ mol-1
2 )   200 kJ mol-1
3 )   300 kJ mol-1
4 )   400 kJ mol-1
see the answer    see the solution

 

149) t1/4 can be taken as the time taken for the concentration of a reactant to drop to 3/4 of its initial value. If the rate constant for a first order reaction is K, the t1/4 can be written as
1 )   0.10 / K
2 )   0.29 / K
3 )   0.69 / K
4 )   0.75 / K
see the answer    see the solution

 

150) An amount of solid NH4HS is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm. pressure. Ammonium hydrogen sulphide decoomposes to yield NH3 and H2S gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to 0.84 atm. The equilibrium constant for NH3HS decomposition at this temperature is
1 )   0.30
2 )   0.18
3 )   0.17
4 )   0.11
see the answer    see the solution

ANSWERS

1) 1
2) 1
3) 2
4) 2
5) 2
6) 2
7) 3
8) 1
9) 2
10) 1
11) 2
12) 3
13) 1
14) 3
15) 2
16) 2
17) 4
18) 1
19) 1
20) 2
21) 2
22) 4
23) 1
24) 3
25) 4
26) 2
27) 1
28) 1
29) 3
30) 4
31) 2
32) 1
33) 4
34) 1
35) 3
36) 3
37) 1
38) 1
39) 1
40) 4
41) 2
42) 3
43) 3
44) 4
45) -
46) -
47) 1
48) 4
49) 3
50) 2
51) 1
52) 3
53) 2
54) 3
55) 4
56) 3
57) 2
58) 2
59) 3
60) 3
61) 2
62) 4
63) 4
64) 4
65) 1
66) 2
67) 2
68) 3
69) 1
70) 3
71) 4
72) 1
73) 4
74) 3
75) 4
76) 4
77) 2
78) 3
79) 1
80) 3
81) 3
82) 1
83) 2
84) 2
85) 1
86) 4
87) 4
88) 1
89) 1
90) 3
91) 2
92) 4
93) 2
94) 1
95) 4
96) 3
97) 1
98) 4
99) 1
100) 2
101) 4
102) 3
103) 3
104) 1
105) 3
106) 1
107) 1
108) 4
109) 2
110) 4
111) 2
112) 4
113) 2
114) 3
115) 1
116) 2
117) 1
118) 3
119) 3
120) 2
121) 3
122) 4
123) 2
124) 3
125) 4
126) 4
127) 3
128) 2
129) 2
130) 3
131) 3
132) 2
133) 2
134) 3
135) 2
136) 1
137) 2
138) 1
139) 2
140) 3
141) 1
142) 1
143) 1
144) 3
145) 2
146) 2
147) 3
148) 2
149) 2
150) 4

Solution

1 back to 1
Refer Terms and definition
2 back to 2
t = ax2 + bx
=> Differentiate both side with respect to time (t)
=> dt/dt = 2ax.dx/dt + b.dx/dt
=> 1 = 2axv + bv
=> v.(2ax + b) = 1
=> (2ax + b) = 1/v
=> Again differentiate both side with respect to time (t)
=> 2a.dx/dt = -v-2 . dv/dt
=> 2av = v-2 . acceleration
=> acceleration = -2av3
3 back to 3
Let Car started from point A.
It traveled for distance S with acceleration f. Assume that point is B
AB = S .................... (i)
Using
v2 = u2 + 2as
vb2 = 0 + 2fS
vb2 = 2fS ..................... (ii)

Next the car traveled for time t at contact speed till point C
So, BC = vbt = (2fS)1/2t

Then the car decelerated at f/2 and come to rest till point D
Using
v2 = u2 + 2as
0 = vb2 - 2.f/2.scd
scd = vb2/f = 2S
AB + BC + CD = 3S
=> S + (2fS)1/2t +2S = 15S
=> (2fS)1/2t = 12 S
=> 2fSt2 = 144 S2
=> S = ft2/72
4 back to 4

Acceleration = (change in velocity)/time
change in velocity = Δv
=> Δv = v2-v1
=> Δv2 = v22 + v12 - 2v1v2cos90°
=> Δv2 = v22 + v12 => Δv2 = 52 + 52 = 50
=> Δv = 5
=> Acceleration = Δv/ 10 => Acceleration = 5/10 = 1/ North-West
5 back to 5
First case when it takes time = t1
Horizontol velocity = vx1
Vertical velocity = vy1
Using formula: v=u+at in vertical direction
vy1 = - vy1 + gt1
2vy1 = gt1 .................. (i)
R = vx1t1 .................. (ii)
vy12 + vx12 = v2 = (gt1/2)2 + (R/t1)2 ....................(iii)

Second case when it takes time = t2
2vy2 = gt2 .................. (iv)
R = vx2t2 .................. (v)
vy22 + vx22 = v2 = (gt2/2)2 + (R/t2)2 ....................(vi)
(iii) and (vi) are equal
=> (gt1/2)2 + (R/t1)2 = (gt2/2)2 + (R/t2)2
=> (gt1/2)2 + (R/t1)2 + gR = (gt2/2)2 + (R/t2)2 + gR
=> gt1/2 + R/t1 = gt2/2 + R/t2
=> (g/2)(t1-t2) = R(t1-t2)/(t1t2)
=> t1t2 = 2R/g
=> So, t1t2 is proportional to R
6 back to 6
Centripetal force on the particle having circular motion = mω2r.
Anular velocity of all the paricles on the ring is same.
Force on outer particle = F1 = mω2R1.
Force on outer particle = F2 = mω2R2.
So, F1/F2 = R1/R2
7 back to 7
On the smooth surface force acting on the block in incline direction = F1
F1 = mgsin45°
Time require to travel distance n = t1
Using formula : s = ut + 1/2 at2
d = 1/2 . gsin45° . t12 ...................(i)

On the rough surface force acting on the block in incline direction = F2
F2 = mgsin45° - f , where f=frictional force
f = μkmgcos45° , where μk = coefficient of friction
F2 = mgsin45° - μmgcos45°
Time require to travel distance n = t2
d = 1/2 . (gsin45° - μk gcos45°) . t22 ..........(ii)
cos45° = cos45°
Divising (ii) and (i)
1 = [(1-μk)t12]/[t22]
We know that: t1/t1 = 1
So, 1 = (1-μk)n2
=> μk = 1 - 1/n2

8 back to 8
Let mass of the block = M
Frictional force in incline plane with inclination Φ = μMgcosΦ
Force due to gravity in the incline plane = MgsinΦ
So acceleration in smooth plane = gsinΦ
Retardation in rough plane = μgcosΦ - gsinΦ
The block will come to rest if acceleration = retardation
gsinΦ = μgcosΦ - gsinΦ
=> μ = 2tanΦ
9 back to 9
Suppose velocity of the bullet is 2y at the time of penetrating the wall
So velocity of the bullet at distance 3cm will be = y
Using, v2 = u2 + 2as
=> u2 = 4u2 + 6a
=> a = -u2/2
Let the bullet further penetrate a distance = x
Using, v2 = u2 + 2as
0 = u2 - 2.u2/2.x
=> x = 1
10 back to 10
Let the velocity of the parachutist after 50 m = y
Using, v2 = u2 + 2as
y2 = 2gs = 2 × 9.81 × 50
Suppose he bailed out at height = h
Using, v2 = u2 + 2as
9 = y2 - 2 × 2 × (h-50)
=> 2 × 9.81 × 50 - 9 = 4(h-50)
=> 4(h-50) = 981 - 9 = 972
=> h = 243 + 50 = 293
11 back to 11
F = -kx
=> ma = -kx
=> 0.3a = -15x
=> a = 50x
=> a = - 50 × 0.2
=> a = - 10 ms-2
12 back to 12
Let the velocity of the body at the time of collision = v
1/2 Mv2 = 1/2 kL2
=> M2v2 = MkL2
=> Mv = momemtum = L
13 back to 13
Initial momemtum = final momentum
Initial momemtum = mV = mVi
Final velocity of mass1 m in i direction = Vx
Final velocity of mass1 m in j direction = Vy Final momemtum of mass1 m = mVxi + mVyj
Final momemtum of mass2 m = mv/j
mvi = mVxi + mVyj + mv/j => mvxi + mVyj = mvi - mV/j
=> mvxi + mVyj = mvi - mV/j
=> Vx = V
=> Vy = -V/
=> Vfinal2 = 1+1/3 = 4/3
=> Vfinal = 2 V /
14 back to 14
Initial energy = Final energy
Initial energy = mgh = 100mg
Final energy = 1/2mv2 + mgh = 1/2mv2 + 20mg
So, 100mg = 1/2mv2 + 20mg
=> v2 = 80g × 2 = 1600
=> v = 40 m/s
15 back to 15
If the incline surface is not moving then
acceleration of the block in inclined plane direction = gsinα

Suppose acceleration of the surface is "a" to keep the block stationary
Due to acceleration of the surface, acceleration block = acosα
In order to keep the block stationary :
acosα = gsinα
a = gtanα

16 back to 16
Mass of semicircular disc = M
Suppose there is a circular disc of mass 2M, then
Moment of intertia of circular disc = 1/2(2M)R2
Moment of intertia of circular disc = 1/2(2M)R2 = MR2
=> So, Moment of intertia of semi-circular disc = (1/2)MR2
17 back to 17
The only force that acts on the body A is gravitational force.
There is no force acting perpendicular to the gravitational force.
So the center of the mass of B and C will not shift.
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Let distance of P from C is = y
P must be the center of mass of the T shaped object.
Assume mass per unit length = 1
So, [Mab × (2l-y)] + [M(2l-y) × (2l-y)/2] = [My × y/2[
=> l × (2l-y) + (2l-y) × (2l-y)/2 = y × y/2
=> 4l2 - 2ly + (2l-y)2 = y2
=> 8l2 -2ly - 4ly = 0
=> 8l2 -6ly = 0
=> y = 4l/3
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Acceleration due to gravity at a depth 'd' from earth surface is :
gd = g(1-   d  )
 R





Acceleration due to gravity at height 'h' from earth surface is :
h is very much smaller than R
gh = g(1-   2h  )
 R





gh = gd
By solving it , d=2h
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Work Done =  GMm  =  6.67 × 10-11 × 100 × 0.01  = 6.67 × 10-10
R 0.1
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Capillary action
The height to which the liquid can be lifted is given by:
h =  2γcosθ
ρgr




where,
γ: liquid-air surface tension(T)(T=energy/area)
θ: contact angle
ρ: density of liquid
g: acceleration due to gravity
r: is radius of tube

When entire arrangement is freely falling then relative acceleration = 0
So, Water will rise to the full length of capillary tube i.e. 20cm

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