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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
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1 )  
17.565 kg ms-1
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2 )  
17.56 kg ms-1
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3 )  
17.57 kg ms-1
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4 )  
17.6 kg ms-1
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| see the answer see the solution |
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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
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1 )  
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2 )  
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3 )  
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4 )  
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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)
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1 )  
500 ms-1
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2 )  
650 ms-1
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3 )  
330 ms-1
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4 )  
460 ms-1
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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.
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1 )  
Statement-1
is true, Statement-2
is true;
Statement-2
is not a correct explanation for
Statement-1
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2 )  
Statement-1
is true, Statement-2
is false
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3 )  
Statement-1
is false, Statement-2
is true
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4 )  
Statement-1
is true, Statement-2
is true;
Statement-2
is a correct explanation for
Statement-1
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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.
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1 )  
Statement-1
is true, Statement-2
is true;
Statement-2
is not a correct explanation for
Statement-1
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2 )  
Statement-1
is true, Statement-2
is false
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3 )  
Statement-1
is false, Statement-2
is true
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4 )  
Statement-1
is true, Statement-2
is true;
Statement-2
is a correct explanation for
Statement-1
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| see the answer see the solution |
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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
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1 )  
3.67 mm
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2 )  
3.38 mm
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3 )  
3.32 mm
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4 )  
3.73 mm
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| see the answer see the solution |
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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
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1 )  
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T1T2
(P1V1 + P2V2)
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P1V1T1 +
P2V2T2
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2 )  
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T1T2
(P1V1 + P2V2)
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P1V1T2 +
P2V2T1
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3 )  
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P1V1T1 +
P2V2T2
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P1V1 + P2V2
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4 )  
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P1V1T2 +
P2V2T1
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P1V1 + P2V2
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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 )
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1 )  
2.4π X 10-4 H
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2 )  
2.4π X 10-5 H
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3 )  
4.8π X 10-4 H
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4 )  
4.8π X 10-5 H
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| see the answer see the solution |
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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?
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1 )  
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2 )  
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3 )  
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4 )  
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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 )
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1 )  
1000 V
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2 )  
2000 V
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3 )  
50 V
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4 )  
500 V
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| see the answer see the solution |
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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)
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1 )  
dcosi = nλdB
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2 )  
dsini = nλdB
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3 )  
2dcosi = nλdB
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4 )  
2dsini = nλdB
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| see the answer see the solution |
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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)?
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1 )  
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2 )  
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3 )  
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4 )  
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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
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1 )  
0.11 km s-1
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2 )  
1.1 km s-1
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3 )  
11 km s-1
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4 )  
110 km s-1
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| see the answer see the solution |
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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?
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1 )  
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2 )  
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3 )  
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4 )  
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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 ?
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1 )  
ρ1 < ρ2 < ρ3
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2 )  
ρ1 < ρ3 < ρ2
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3 )  
ρ3 < ρ2 < ρ1
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4 )  
ρ1 > ρ3 > ρ2
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| see the answer see the solution |
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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 ?
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1 )  
It is a pnp transistor with R as emitter
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2 )  
It is an npn transistor with R as collector
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3 )  
It is an npn transistor with R as base
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4 )  
It is a pnp transistor with R as collector
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| see the answer see the solution |
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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
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1 )  
0.67 J
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2 )  
0.34 J
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3 )  
0.16 J
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4 )  
1.00 J
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| see the answer see the solution |
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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
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1 )  
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2 )  
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3 )  
α = 25.00 π , β = π
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4 )  
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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
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1 )  
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2 )  
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3 )  
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4 )  
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| see the answer see the solution |
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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
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1 )  
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ρ I
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-
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ρ I
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2 π a
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2 π a (a + b)
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2 )  
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3 )  
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ρ I
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-
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ρ I
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π a
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π a (a + b)
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4 )  
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| see the answer see the solution |
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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
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1 )  
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2 )  
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3 )  
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4 )  
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22)
An experiment is performed to find the refractive
index of glass using a travelling microscope.
In this experiment distances are measured by
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1 )  
a meter scale provided on the microscope
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2 )  
a screw gauge provided on the microscope
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3 )  
a vernier scale provided on the microscope
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4 )  
a standard laboratory scale.
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| see the answer see the solution |
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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 )
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1 )  
5 X 10-6 T southward
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2 )  
2.5 X 10-7 T northward
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3 )  
2.5 X 10-7 T southward
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4 )  
5 X 10-6 T northward
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| see the answer see the solution |
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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

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1 )  
0.03 A P2 to P1
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2 )  
0.27 A P1 to P2
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3 )  
0.27 A P2 to P1
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4 )  
0.03 A P1 to P2
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| see the answer see the solution |
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25)
The dimension of magnetic field in
M, L, T and C (Coulomb) is given as
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1 )  
M T -1C-1
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2 )  
M T-2C-1
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3 )  
M L T-1C-1
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4 )  
M T2C-2
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| see the answer see the solution |
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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
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1 )  
40.5 pF
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2 )  
20.25 pF
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3 )  
1.8 pF
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4 )  
45 pF
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| see the answer see the solution |
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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
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1 )  
20,000 J - 50,000 J
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2 )  
2,000 J - 5,000 J
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3 )  
200 J - 500 J
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4 )  
2 X 105 J - 3 X 105 J
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| see the answer see the solution |
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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
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1 )  
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2 )  
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3 )  
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4 )  
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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

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1 )  
110 Ω
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2 )  
55 Ω
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3 )  
13.75 Ω
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4 )  
220 Ω
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| see the answer see the solution |
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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
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1 )  
54 > x > 36
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2 )  
36 > x > 18
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3 )  
18 > x
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4 )  
x > 54
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| see the answer see the solution |
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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?
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1 )  
εr =0.5 , μr = 0.5
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2 )  
εr =1.5 , μr = 1.5
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3 )  
εr =0.5 , μr = 1.5
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4 )  
εr =1.5 , μr = 0.5
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| see the answer see the solution |
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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?
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1 )  

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2 )  

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3 )  

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4 )  

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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?
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1 )  

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2 )  

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3 )  

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4 )  

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

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1 )  
NAND gate
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2 )  
OR gate
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3 )  
NOR gate
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4 )  
AND gate
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| see the answer see the solution |
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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?
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1 )  
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2 )  
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3 )  
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4 )  
Tn independent of n , rn ∝ n
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| see the answer see the 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
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2 back to 2
Moment of Intertia of a body is the intertia of a rotating body with respect
to the axis of rotation.
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Moment of interia of the square plate at the center of the axis (virtical axis) =
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ma2
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6
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Moment of interia at th axis passing thru corner = Icenter + m d2 =
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ma2
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+ m(
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a
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)2
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=
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2
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ma2
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6
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3
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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
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4 back to 4
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5 back to 5
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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
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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
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T1T2
(P1V1 + P2V2)
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P1V1T2 +
P2V2T1
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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
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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
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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
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λ =
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h
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2meV = (h/λ)2
29.12 x 10-50 V = ((6.6 x 10-34)/λ)2
Vλ2 = 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.
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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
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12 back to 12
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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
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14 back to 14
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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
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16 back to 16
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17 back to 17
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18 back to 18
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19 back to 19
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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
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ρ I
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-
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ρ I
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2 π a
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2 π a (a + b)
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..................... (i)
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In the sanme way, VC-VB due to current I at point D will be
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-
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ρ I
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+
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ρ I
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..................... (ii)
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2 π a
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2 π a (a + b)
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By adding (i) and (ii)
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VB-VC =
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ρ I
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-
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ρ I
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π a
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π a (a + b)
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21 back to 21
Surface area of hemisphere = 2πr2
ρ(I/2πr2)
VB-VC due to current I at point A will be
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Therefore, E = ρj =
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ρI
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2πr2
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22 back to 22
a vernier scale provided on the microscope
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23 back to 23
Magnetic Field around a wire (B)
where
I = current
r = distance from wire
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B =
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4 π X 10-7 x 100
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= 5 x 10-6 southward
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2 x π x 4
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Direction is southward: Try to do cross product between the direction of current and radius.
You will get the direction as southward.
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24 back to 24
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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
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26 back to 26
Parallel Plate Capacitor
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
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C = 9pF = ε0
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A
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............................. (i)
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d
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After applying the dielectric, assume that the equivalent capacitance is = C
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1
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=
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1
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+
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1
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=
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d/3
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+
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2d/3
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............................. (ii)
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C
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C1
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C2
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Aε0κ1
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Aε0κ2
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Replace κ1=3 and κ1=6 and solve (i) and (ii)
The equivalent capacitance C = 40.5 pF
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27 back to 27
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Kinetic Entergy (K) =
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1
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m v2
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2
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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
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28 back to 28
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29 back to 29
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30 back to 30
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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.
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32 back to 32
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33 back to 33
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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.
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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,
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Kinetic Energy=
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1
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mv2 =
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k
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= Constant, so Tn independent of n
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2
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2
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As per Bohr's model
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L = (angular momentum)
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nh
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2 π
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=
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nh
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So r is proportional to n (h is constant (Planck's constant))
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2 π
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