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AIEEE Home page 2008 AIEEE PAPER - (Physics)

 

1) A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms-1. The magnitude of its momentum is recorded as
1 )   17.565 kg ms-1
2 )   17.56 kg ms-1
3 )   17.57 kg ms-1
4 )   17.6 kg ms-1
see the answer    see the solution

 

2) Consider a uniform square plate of side 'a' and mass 'm'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
1 )  
1   m a2
12
2 )  
7   m a2
12
3 )  
2   m a2
3
4 )  
5   m a2
6
see the answer    see the solution

 

3) The speed of sound in oxygen (O2) at a certain temperature is 460 ms-1. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)
1 )   500 ms-1
2 )   650 ms-1
3 )   330 ms-1
4 )   460 ms-1
see the answer    see the solution

 

4) This question contains Statement-I and Statement2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-1:
Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. and
Statement-2:
For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decreases with increasing Z.

1 )   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
2 )   Statement-1 is true, Statement-2 is false
3 )   Statement-1 is false, Statement-2 is true
4 )   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
see the answer    see the solution

 

5) This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-1:
For a mass M kept at the centre of a cube of side 'a', the flux of gravitational field passing through its sides is 4π GM. and
Statement-2:
If the direction of a field due to a point source is radial and its dependence on the distance 'r' from the source is given as 1/r2 , its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

1 )   Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
2 )   Statement-1 is true, Statement-2 is false
3 )   Statement-1 is false, Statement-2 is true
4 )   Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
see the answer    see the solution

 

6) Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of -0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is
1 )   3.67 mm
2 )   3.38 mm
3 )   3.32 mm
4 )   3.73 mm
see the answer    see the solution

 

7) An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure P1 and temperature T1. The other chamber has volume V2 and temperature T2. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
1 )  
T1T2 (P1V1 + P2V2)
P1V1T1 + P2V2T2
2 )  
T1T2 (P1V1 + P2V2)
P1V1T2 + P2V2T1
3 )  
P1V1T1 + P2V2T2
P1V1 + P2V2
4 )  
P1V1T2 + P2V2T1
P1V1 + P2V2
see the answer    see the solution

 

8) Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area A = 10 cm2 and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is

( μ0 = 4π X 10-7 T m A-1 )

1 )   2.4π X 10-4 H
2 )   2.4π X 10-5 H
3 )   4.8π X 10-4 H
4 )   4.8π X 10-5 H
see the answer    see the solution

 

9) A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?
1 )  
2 )  
3 )  
4 )  
see the answer    see the solution

 

10) Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure)

Electrons accelerated by potential V are diffracted from a crystal. If d = 1 Å and i = 30° , V should be about ( h = 6.6 X 10-34 Js, me = 9.1 X 10-31 Ks, e = 1.6 X 10-19 C )

1 )   1000 V
2 )   2000 V
3 )   50 V
4 )   500 V
see the answer    see the solution

 

11) Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure)

If a strong diffraction peak is observed when electrons are incident at an angle 'i' from the normal to the crystal planes with distance 'd' between them (see figure), de Broglie wavelength λdB of electrons can be calculated by the relationship (n is an integer)

1 )   dcosi = nλdB
2 )   dsini = nλdB
3 )   2dcosi = nλdB
4 )   2dsini = nλdB
see the answer    see the solution

 

12) Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure)

In an experiment, electrons are made to pass through a narrow slit of width 'd' comparable to their de Broglie wavelength. They are detected on a screen at a distance 'D' from the slit (see figure)

Which of the following graphs can be expected to represent the number of electrons 'N' detected as a function of the detector position 'y' (y = 0 corresponds to the middle of the slit)?

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

 

13) A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s-1, the escape velocity from the surface of the planet would be
1 )   0.11 km s-1
2 )   1.1 km s-1
3 )   11 km s-1
4 )   110 km s-1
see the answer    see the solution

 

14) A thin rod of length 'L' is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as k(x/L)n , where n can be zero or any positive number. If the position xCM of the centre of the mass of the rod is plotted against 'n', which of the following graphs best approximates the dependence of xCM on n?
1 )  
2 )  
3 )  
4 )  
see the answer    see the solution

 

15) A Jar is filled with two non-mixing liquids 1 and 2 having densities ρ1 and ρ2, respectively, A solid ball, made of a material of density ρ2, is dropped in the jar. It comes to equilibrium in the position shown in the figure.

which of the following is true for ρ1 , ρ2 and ρ3 ?
1 )   ρ1 < ρ2 < ρ3
2 )   ρ1 < ρ3 < ρ2
3 )   ρ3 < ρ2 < ρ1
4 )   ρ1 > ρ3 > ρ2
see the answer    see the solution

 

16) A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q. some resistance is seen on the multimeter. Which of the following is true for the transistor ?
1 )   It is a pnp transistor with R as emitter
2 )   It is an npn transistor with R as collector
3 )   It is an npn transistor with R as base
4 )   It is a pnp transistor with R as collector
see the answer    see the solution

 

17) A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is
1 )   0.67 J
2 )   0.34 J
3 )   0.16 J
4 )   1.00 J
see the answer    see the solution

 

18) A wave travelling along the x-axis is described by the equation y(x,t) = 0.005 cos (αx - βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are
1 )  
α =   0.04   , β =   1.0
π π
2 )  
α = 12.50 π   , β =   π
2.0
3 )   α = 25.00 π   , β = π
4 )  
α =   0.08   , β =   2.0
π π
see the answer    see the solution

 

19) A student measures the focal length of a convex lens by putting an object pin at a distance 'u' from the lens and measuring the distance 'v' of the image pin. The graph between 'u' and 'v' plotted by the student should look like
1 )  
2 )  
3 )  
4 )  
see the answer    see the solution

 

20) Consider a block of conducting material of resistivity 'ρ' shown in the figure. Current 'I' enters at 'A' and leaves from 'D'. We apply superposition principal to find voltage 'ΔV' developed between 'B' and 'C' . The calculation is done in the following steps:
(i) Take current 'I' entering from 'A' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance 'r' from A by using Ohm's law E = ρ j , where 'j' is the current per unit area at 'r'.
(iii) From the 'r' dependence of E(r), obtain the potential V(r) at 'r'
(iv) Repeat (i), (ii) and (iii) for current 'I' leaving 'D' and superpose results for 'A' and 'D'.

Δ V measured between B and C is

1 )  
ρ I   -   ρ I
2 π a 2 π a (a + b)
2 )  
ρ I
2 π a (a - b)
3 )  
ρ I   -   ρ I
π a π a (a + b)
4 )  
ρ I   -   ρ I
a (a + b)
see the answer    see the solution

 

21) Consider a block of conducting material of resistivity 'ρ' shown in the figure. Current 'I' enters at 'A' and leaves from 'D'. We apply superposition principal to find voltage 'ΔV' developed between 'B' and 'C' . The calculation is done in the following steps:
(i) Take current 'I' entering from 'A' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance 'r' from A by using Ohm's law E = ρ j , where 'j' is the current per unit area at 'r'.
(iii) From the 'r' dependence of E(r), obtain the potential V(r) at 'r'
(iv) Repeat (i), (ii) and (iii) for current 'I' leaving 'D' and superpose results for 'A' and 'D'.

For current entering at A, the electric field at a distance 'r' from A is

1 )  
ρ I
2 π r2
2 )  
ρ I
4 π r2
3 )  
ρ I
8 π r2
4 )  
ρ I
r2
see the answer    see the solution

 

22) An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by
1 )   a meter scale provided on the microscope
2 )   a screw gauge provided on the microscope
3 )   a vernier scale provided on the microscope
4 )   a standard laboratory scale.
see the answer    see the solution

 

23) A horizontal overhead powerline is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is ( μ0 = 4 π X 10-7 T m A-1 )
1 )   5 X 10-6 T southward
2 )   2.5 X 10-7 T northward
3 )   2.5 X 10-7 T southward
4 )   5 X 10-6 T northward
see the answer    see the solution

 

24) A 5V battery with internal resistance 2Ω and a 2V battery with internal resistance 1Ω are connected to a 10Ω resistor as shown in the figure. The current in the 10Ω resistor is

1 )   0.03 A   P2 to P1
2 )   0.27 A   P1 to P2
3 )   0.27 A   P2 to P1
4 )   0.03 A   P1 to P2
see the answer    see the solution

 

25) The dimension of magnetic field in M, L, T and C (Coulomb) is given as
1 )   M T -1C-1
2 )   M T-2C-1
3 )   M L T-1C-1
4 )   M T2C-2
see the answer    see the solution

 

26) A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is 'd'. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant κ1 = 3 and thickness d/3 while the other one has dielectric constant κ2 = 6 and thickness 2d/3. Capacitance of the capacitor is now
1 )   40.5 pF
2 )   20.25 pF
3 )   1.8 pF
4 )   45 pF
see the answer    see the solution

 

27) An athlete in the olympic games covers a distance of 100m in 10s. His kinetic energy can be estimated to be in the range
1 )   20,000 J - 50,000 J
2 )   2,000 J - 5,000 J
3 )   200 J - 500 J
4 )   2 X 105 J - 3 X 105 J
see the answer    see the solution

 

28) A spherical solid ball of volume V is made of a material of density ρ1. It is falling through a liquid of density ρ2 ( ρ2 < ρ1 ) Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v , i.e. Fviscous = -kv2(k > 0). The terminal speed of the ball is
1 )  
2 )  
V g ( ρ1 - ρ2 )
k
3 )  
4 )  
V g ρ1
k
see the answer    see the solution

 

29) Shown in the figure is a meter-bridge set up with null deflection in the galvanometer. T he value of the unknown resistor R is

1 )   110 Ω
2 )   55 Ω
3 )   13.75 Ω
4 )   220 Ω
see the answer    see the solution

 

30) While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then
1 )   54 > x > 36
2 )   36 > x > 18
3 )   18 > x
4 )   x > 54
see the answer    see the solution

 

31) Relative permittivity and permeability of a material are εr and μr respectively. Which of the following values of these quantifies are allowed for a diamagnetic material?
1 )   εr =0.5 , μr = 0.5
2 )   εr =1.5 , μr = 1.5
3 )   εr =0.5 , μr = 1.5
4 )   εr =1.5 , μr = 0.5
see the answer    see the solution

 

32) A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range
0 ≤ r < ∞
where r is the distance from the centre of the shell?
1 )  

2 )  

3 )  

4 )  

see the answer    see the solution

 

33) A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x direction with a constant speed. The position of the first body is given by x1(t) after time t and that of the second body by x2(t) after the same time interval. Which of the following graphs correctly describes (x1 - x2) as a function of time t?
1 )  

2 )  

3 )  

4 )  

see the answer    see the solution

 

34) In the circuit shown, A and B represent two inputs and C represents the output. The circuit represents

1 )   NAND gate
2 )   OR gate
3 )   NOR gate
4 )   AND gate
see the answer    see the solution

 

35) Suppose an electron is attracted towards the origin by a force k/r where 'k' is a constant and 'r' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be 'rn' and the kinetic energy of the electron to be 'Tn'. Then which of the following is true?
1 )  
Tn ∝   1   ,   rn ∝ n
n
2 )  
Tn ∝   1   ,   rn ∝ n2  
n
3 )  
Tn ∝   1   ,   rn ∝ n2  
n2
4 )   Tn independent of n , rn ∝ n
see the answer    see the solution

ANSWERS

1) 42) 33) none4) 2
5) 46) 27) 28) 1
9) 110) 311) 312) 1
13) 414) 215) 216) 3
17) 118) 319) 120) 3
21) 122) 323) 124) 1
25) 126) 127) 228) 3
29) 430) 431) 432) 3
33) 434) 235) 4

Solution

1 back to 1
Momemntum = mass x velocity
Momemntum = 3.513 x 5.00 = 17.565 kg m sec-1
Momemntum in three significant digit = 17.6 kg m sec-1
2 back to 2
Moment of Intertia of a body is the intertia of a rotating body with respect to the axis of rotation.
Moment of interia of the square plate at the center of the axis (virtical axis) =  ma2
6

Moment of interia at th axis passing thru corner = Icenter + m d2 ma2  + m(  a  )2  =  2  ma2
6 3
3 back to 3
Speed of the sound in gas

R = gas constant(8.314 J/mol K)
T = the absolute temperature
M = the molecular weight of the gas (kg/mol)
γ = adiabatic constant = cp/cv
γO2 = 7/5
γHe = 5/3
MO2 = 32
MHe = 4
......(i)
......(ii)
By solving (i) and (ii) VHe = 1419 m sec-1
4 back to 4
5 back to 5
6 back to 6
Two full turns of the circular scale of a screw gauge cover a distance of 1 mm .
Therrefore one full turns of the circular scale of a screw gauge cover a distance of 0.5 mm .
Reading = MSR + CSR x LC - error L.C (least count) = 0.5/50 = 0.01
So the diameter of wire = 3mm + 35 x L.C - (-0.03)
the diameter of wire = 3mm + 35 x 0.01 mm + 0.03mm
the diameter of wire = 3.38
7 back to 7
Internal entergy of ideal gas (U) = cvnRT
Assume the final temperature = T
Internal energy of first gas before removing the partition = cvn1RT1
Internal energy of second gas before removing the partition = cvn2RT2
Internal energy of first gas after removing the partition = cvn1RT
Internal energy of second gas after removing the partition = cvn2RT
Change in energy of first gas = cvn1RT - cvn1RT1
Change in energy of second gas = cvn2RT - cvn2RT2
As the container is insulated, so total change of energy = 0
(cvn1RT - cvn1RT1 ) + (cvn2RT - cvn2RT2 ) = 0
n1R(T - T1) + n2R(T - T2 ) = 0 .........(i)

n1R= P1V1/T1 .........(ii)
n2R= P2V2/T2 .........(iii)
By solving (i),(ii) and (iii) you get the answer as
T1T2 (P1V1 + P2V2)
P1V1T2 + P2V2T1
8 back to 8
Mutual inductance of two solenoid two long thin solenoids, one wound on top of the other
M = μ0N1N2LA
N1 = total number of turns per unit length for first solenoid
N2 = number of turns per unit length for second solenoid
A = cross-sectional area
L = length of the solenoid.

A = 10cm2 = 10/10000 = 0.001m2
L = 20cm = 0.2 m
N1 (turns per unit length) = 300/0.2 = 1500
N2 (turns per unit length) = 400/0.2 = 2000
M = 4π x 10-7 x 1500 x 2000 x 0.001 x 0.2
M = 2.4π x 10-4 H

9 back to 9
Soap solution has less surface tension than water.
Soap solution and water have almost same density.
As water has more surface tension so it has more height.

Refer following formula
The height to which the liquid can be lifted is given by
h=height of the liquid lifted
T=surface tension
r=radius of capillary tube
h=  2T
ρrg

10 back to 10
As per Bragg's law
nλ = 2d sinθ

where
θ = angle between the surface and the ray = 90-30=60°
nλ = 2 . 10-10 . sin30°
(nλ)2 = 3 x 10-20
As per Davisson and Germer experiment
λ =  h  
 






2meV = (h/λ)2
29.12 x 10-50 V = ((6.6 x 10-34)/λ)2
2 = 1.496 x 10-18
V x 3 x 10-20 = 1.496 x 10-18 n2
V = 50 n2
n → it is integer value (it can 1,2,3,4,...)
If we replace n=1 then we get V = 50.

11 back to 11
As per Bragg's law
nλ = 2d sinθ

where
n = integer (based upon order)
λ = wavelength
d = distance between the planes
θ = angle between the surface and the ray

So,
θ = 90° - i
nλ = 2d sin(90°-i)
nλ = 2d cosi

12 back to 12
13 back to 13
Escape velocity
Escape velocity from a body of mass M and radius r is

So escape velocity is directly proportional to root of mass and inversely proportional to root of radius
So the escape velocity from the surface of the planet would be
Ve = 11 x x
Ve = 110 km s-1
14 back to 14
15 back to 15
ρ2 has the maximum density as it is at the bottom
ρ1 has the least density as it is at the top
Therefore , ρ1 < ρ3 < ρ2
16 back to 16
17 back to 17
18 back to 18
19 back to 19
20 back to 20
Surface area of hemisphere = 2πr2

E = ρ j = ρ(I/2πr2)

By solving above equation
VB-VC due to current I at point A will be
ρ I   -   ρ I
2 π a 2 π a (a + b)   ..................... (i)







In the sanme way, VC-VB due to current I at point D will be
ρ I   +   ρ I   ..................... (ii)
2 π a 2 π a (a + b)







By adding (i) and (ii)
VB-VC =   ρ I   -   ρ I
π a π a (a + b)

21 back to 21
Surface area of hemisphere = 2πr2

ρ(I/2πr2) VB-VC due to current I at point A will be
j=  I
2πr2







Therefore, E = ρj =  ρI
2πr2

22 back to 22
a vernier scale provided on the microscope
23 back to 23
Magnetic Field around a wire (B)
B = μ0 I
2 π r

where
I = current
r = distance from wire
B =  4 π X 10-7 x 100 = 5 x 10-6 southward
2 x π x 4
Direction is southward: Try to do cross product between the direction of current and radius. You will get the direction as southward.
24 back to 24
25 back to 25
Magnetic field is a vector field in a space that exert force on a moving electic charge. Init of magnetic field strength is Tesla.
One Tesla is a strength measured as force (Newton) on a wire of unit length (meter) with unit electric current(Ampere). Nm-1A-1
MT-1C-1
26 back to 26
Parallel Plate Capacitor
C = 9pF = κ ε0   A 
d
where
C = [Farad (F)]
κ = dielectric constant
A = Area of plate
d = distance between the plate
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)

Initially there was no dielectric, so κ = 1, so
C = 9pF = ε0   A    ............................. (i)
d
After applying the dielectric, assume that the equivalent capacitance is = C
1  =  1  +  1  =  d/3  +  2d/3   ............................. (ii)
C C1 C2 0κ1 0κ2
Replace κ1=3 and κ1=6 and solve (i) and (ii)
The equivalent capacitance C = 40.5 pF

27 back to 27
Kinetic Entergy (K) =  1   m v2
2







Mass of athlete is between 45 to 90 kg.
Assume mass of athlete is between 70 kg.
velocity of athlete 100/10 = 10 m/sec
K = 1/2 x 70 x 10 x 10 = 3500 J
So answer is 2,000 J - 5,000 J
28 back to 28
29 back to 29
30 back to 30
31 back to 31
εr is greater than one for any type of material
Value of μr is between 1 and 0 for diamagnetic material.
32 back to 32
33 back to 33
34 back to 34
The current will flow into the resistor if any of the input (A or B) has the value as 1 (i.e. TRUE).
The current will NOT flow into the resistor if both the input (A or B) has the value as 0 (i.e. FALSE).
A(true) OR B(true) : current will flow into the resistor
A(true) OR B(false) : current will flow into the resistor
A(false) OR B(true) : current will flow into the resistor
A(false) OR B(false) : current will NOT flow into the resistor

So the circuit is OR.

35 back to 35
Electron is attracted towards the origin by a force k/r where 'k' is a constant and 'r' is the distance
Therefore,
k  =  mv2
r r
Kinetic Energy=  1  mv2 k  =  Constant, so Tn independent of n
2 2
As per Bohr's model
L = (angular momentum)  nh
2 π
mvr =  nh
2 π
 =  nh   So r is proportional to n (h is constant (Planck's constant))
2 π
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