GATE Physics Mock Test Series - 8 - Physics MCQ

# GATE Physics Mock Test Series - 8 - Physics MCQ

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## 30 Questions MCQ Test GATE Physics Mock Test Series 2025 - GATE Physics Mock Test Series - 8

GATE Physics Mock Test Series - 8 for Physics 2024 is part of GATE Physics Mock Test Series 2025 preparation. The GATE Physics Mock Test Series - 8 questions and answers have been prepared according to the Physics exam syllabus.The GATE Physics Mock Test Series - 8 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for GATE Physics Mock Test Series - 8 below.
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GATE Physics Mock Test Series - 8 - Question 1

### The entropy of a system, S, is related to the accessible phase space volume G by S = kBlnG(E, N, V) where E, N and V are the energy, number of particles and volume respectively. From this one can conclude that G

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 1

Two macroscopic system, which are in thermal contact, the required condition for the equilibrium is that their b parameter must be equal.
accessible phase space volume
So

on comparing
S = klnr(E,V,N)
and it is obvious that at equilibrium the accessible phase volume is maximum.

GATE Physics Mock Test Series - 8 - Question 2

### Let dw be the work done in a quasistatic reversible thermodynamic process. Which of the following statements about dw is correct?

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 2

The first law of thermodynamics can be given
dQ = dU + dW
here dQ and dW both are path function and dU is state function. For making dW a perfect differential, we take dQ = 0
So dU + dW = 0
dW = -dU
and dQ = 0 occur in adiabatic process, so, dW0 is a perfect differential if the process is adiabatic.

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GATE Physics Mock Test Series - 8 - Question 3

### A vector perpendicular to any vector that lies on the plane defined by x + y + z = 5, is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 3

For finding the vector which is perpendicular to any vector on the plane is given by taking the gradient of that plane eqn.
The plane is φ = x - y + z - 5

GATE Physics Mock Test Series - 8 - Question 4

The eigenvalues of the matrix A  are

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 4

GATE Physics Mock Test Series - 8 - Question 5

Two events, separated by a (spatial) distance 9 x 109 m, are simultaneous in one inertial frame. The time interval between these two events in a frame moving with a constant speed 0.8 c (where the speed of light c = 3 x 108 m/s) is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 5

Time measured at A,
Time measured at B,

GATE Physics Mock Test Series - 8 - Question 6

The commutator [x2, p2] is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 6

[ x2,p2] = [ x2,pp] = p [ x2,p ] + [ x2,p ]p
Since [A, BC] = B [A, C] + [A, B] C

GATE Physics Mock Test Series - 8 - Question 7

Consider three polarizers P1 ,P2 and P3 placed along an axis as shown in the figure

The pass axis of P1 and P3 are at right angles to each other while the pass axis of P2 makes an angle θ with that of P1 . A beam of unpolarized light of intensity l0 is incident on P1 as shown . The intensity of light emerging from P3 is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 7

According to malus law the transmitted light intensity is proportional to the square of cosine of angle between polarizer and analyzer.

when light say passing through P1 the angle is q = 0° so
.....(A)
when this polarized light passing through P2 which makes an angle q with P1 and P2 so
....(B)
Now P1 and P3 are 1 to each other so according to malus law the transmitted intensity

GATE Physics Mock Test Series - 8 - Question 8

A point particle of mass m carrying an electric charge q is attached to a spring of stiffness constant k. A constant electric field E along the direction of the spring is switched on for a time interval T(whereT  Neglecting radiation loss, the amplitude of oscillation after the field is switched off is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 8

Let, in presence of electric field, the spring elongates by; distance ‘y’

The direction of motion is along y direction, then equation of motion is,

Now,

Now, apply boundary conditions, at t = 0, y = 0

where,
Now, the amplitude of oscillation is,

GATE Physics Mock Test Series - 8 - Question 9

A transistor with β = 100 is used in CE configuration. The collector circuit resistance is 1kΩ& V= 20v. Assuming Vbe = 0 find the value of collector to base resistance such that quiescent collector to emitter voltage is 4v

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 9

GATE Physics Mock Test Series - 8 - Question 10

The phenomenon known as ‘Early effect’ in a bipolar transistor refers to a reduction of the effective-basewidth caused by___

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 10

In a bipolar transistor, the increase in the depletion region of the reverse biased junction, tends to decrease the width of the base with increased reverse voltage. This in turn causes the current gain to increase with increased voltage resulting in a nearly linear increase in current even with the device in the saturation.

GATE Physics Mock Test Series - 8 - Question 11

A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant, r is the distance of the bead from the origin. The momentum conjugate to r is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 11

The momentum conjugate to r is =

GATE Physics Mock Test Series - 8 - Question 12

A particle of mass m is in a potential given by

where a and r0 are positive constants. When disturbed slightly from its stable equilibrium position, it undergoes a simple harmonic oscillation. The time period of oscillation is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 12

where a & r0 is positive constant

For stable equilibrium

We know that the time period of oscillation is

where K is force constant

GATE Physics Mock Test Series - 8 - Question 13

A planet of mass m moves in a circular orbit of radius r0 in the gravitational potential V(r) =  where k is a positive constant. The orbital angular momentum of the planet is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 13

Gravitational potential
Gravitational Force (F)

momentum (p) = mv =
Anglax momentum(L)  =

GATE Physics Mock Test Series - 8 - Question 14

The solution of the differential equation

subject to the boundary conditions y(0) = 1 and y(∞) = 0, is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 14

The differential equation

according to boundary conditions; y(0) = 1

equation 3 will be satisfy if or only if

{adding and subtracting e1/2}

GATE Physics Mock Test Series - 8 - Question 15

In an interference pattern formed by two coherent sources, the maximum and the minimum of the intensities are 9I0 and I0, respectively. The intensities of the individual waves are

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 15

The max & min intensities by two coherent sources is given by:-

Solving the above two eq, we get
l1 = 4l0       &       l2 = l0

GATE Physics Mock Test Series - 8 - Question 16

Identify the CORRECT statement for the following vectors

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 16

The determinate is not equal to zero

have no mutual relation so it is linearly independent

GATE Physics Mock Test Series - 8 - Question 17

Identify, the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, ED and EF are conduction band, valence band, impurity level and Fermi level, respectively.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 17

As doping with Arsenic Will change the pure silicon Semiconductor into n - type & in n - type SC the free charge carriers are present does to CB because Arsenic is a pentavalent atom thus the atom Thus the fermi Energy level will lie slightly above the middle of the Energy gap & does to ED.

GATE Physics Mock Test Series - 8 - Question 18

A pendulum suspended from the ceiling of the train is at rest. What will be the time period of pendulum if the train accelerates at 10 m/s2 (Take g = 10 m/s2)

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 18

For simple pendulum T =
T = 2 se.                   ......(B)
So, from eq.(A) and (B),

GATE Physics Mock Test Series - 8 - Question 19

A rod of proper length l0 oriented parallel to the x-axis moves with speed 2c/3 along the x-axis in the. S-frame, where c is the speed of the light in free space. The observer is also moving along the x-axis with speed c/2 with respect to the S-frame. The length of the rod as measured by the observer is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 19

For finding the length of rod firstly finding the relativistic velocity which is equal to

Now the measured length

GATE Physics Mock Test Series - 8 - Question 20

Given  is a constant vector and r is the position vector. The value of   where C is a circle of unit radius centered at origin is _____ .

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 20

GATE Physics Mock Test Series - 8 - Question 21

A system has two energy levels with energies ε and 2ε. The lower is 4-fold degenerate while the upper level is doubly degenerate. If there are N noninteracting classical particles in the system, which is in thermodynamic equilibrium at a temperature T, the fraction of particles in the upper level is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 21

So, partition function Z =

so, fraction of particles in the upper level is

GATE Physics Mock Test Series - 8 - Question 22

A spherical conductor of radius a is placed in a uniform electric field  the potential at a point  for r > a, is given by

where r is the distance of P from the centre O of the sphere and q is the angle OP makes with the z-axis.

The charge density on the sphere at q = 30° is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 22

Potential f (r, θ )
We know electric field due to conducting sphere is

E F. at the surface sphere of sphere and at θ = 30°

So, surface charge density s

GATE Physics Mock Test Series - 8 - Question 23

The solution of the differential equation for  subject to the initial conditions  is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 23

So, solution of differential equation
y(t) =t sin h (t)

GATE Physics Mock Test Series - 8 - Question 24

A particle of mass m is confined in the potential

Let the wave function of the particle be given by

where y0 and y1 are the eigen functions of the ground state and the first excited state respectively. The expectation value of the energy is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 24

y0 ground state eigen function y,® first excited state eigen function energy eigen value E =(n+1/2)ℏω

for ground state n = 0, E =
for first excited state n =1, E =

GATE Physics Mock Test Series - 8 - Question 25

Two magnetic dipoles of magnitude m each placed in a plane as shown. The energy of interaction is given by

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 25

Angle between dipoles = 90°
Angles made by diploes with position vector (d) = 45 °
Magnetic interaction energy
U = M.B

GATE Physics Mock Test Series - 8 - Question 26

A mass m is constrained to move on a horizontal frictionless surface. It is set in circular m otion with radius r0 and angular speed w0 by an applied force com municated through an inextensible thread that passes through a hole on the surface as shown in the figure. This force is then suddenly doubled. The magnitude of the radial velocity of the mass

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 26

The particle is moving in a circular motion with radius r0 and angular speed ω0 by an applied force F applied through an inextensible thread passing through hole.
The circular motion of the particle is,
Now. when we doubled the force.

Subtract equation (A) from (B). we get

As the force increases, r will decrease and hence, velocity of particle will decrease till the fall into the hole.

GATE Physics Mock Test Series - 8 - Question 27

For the BJT circuit shown, assume that the β of the transistor is very large and VBE = 0.7V. The mode of operation of the BJT is ___

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 27

For saturation, VBE > 0.7 volts In saturation condition,

Apply KVL in base circuit

So, operate in saturation region.

GATE Physics Mock Test Series - 8 - Question 28

If for a silicon n-p-n transistor, the base-to-emitter voltage (VBE) is 0.7V and the collector-to-base voltage (VCB) is 0.2V. then the transistor is operating in the___

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 28

VB = 0.7V [Forward-biased]
and VBC = -VCB = - 0.2V (Reverse-biased)
Hence, the transistor operates normal active mode.

GATE Physics Mock Test Series - 8 - Question 29

Assuming VCEsat = 0.2V and β= 50. the minimum base current (lB) required to drive the transistor in the given figure to saturation is___

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 29

The minimum value of base current to derive the transistor into saturation is

From the figure given ,

GATE Physics Mock Test Series - 8 - Question 30

In the voltage regulator shown in the given figure, the load current can vary from 100 mAto 500 mA. Assuming that the Zener diode is ideal (i.e, the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of R is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 30

From the circuit given, we have

( Zener knee current is negligibly small)
or- 14Ω < R < 70Ω
Hence, required value of R = 14Ω [closed min value]

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