GATE Physics Mock Test Series - 2 - Physics MCQ

GATE Physics Mock Test Series - 2 - Physics MCQ

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30 Questions MCQ Test - GATE Physics Mock Test Series - 2

GATE Physics Mock Test Series - 2 for Physics 2024 is part of Physics preparation. The GATE Physics Mock Test Series - 2 questions and answers have been prepared according to the Physics exam syllabus.The GATE Physics Mock Test Series - 2 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 - 2 below.
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GATE Physics Mock Test Series - 2 - Question 1

Consider a beam of plane polarised light of wavelength λ is incident on a optical component making angle 45° to the optical axis and output light is circularly polarised then the optical component is

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 1

For quarter wave plate

n = 0,1,2, 3.......
When a plane polarised light is incident on quarter wave plate with angle θ= 45° then output light is circularly polarised.

GATE Physics Mock Test Series - 2 - Question 2

A complex matrix is given as  then

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

So , A+ = A
This implies that A is Hermitian matrix and all  eigen values of Hermittian matrix are real.

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GATE Physics Mock Test Series - 2 - Question 3

A particle of mass m, moves under the action of a central force whose potential is V(r) = kmr3 (k > 0 ) , then the angular frequency is _________ .

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 3

For angular frequency, we have to find out equation of motion. We use Taylor's series expansion

V(r) = Kmr3
Ve =

So at r = r0

T =

ω = √ 5Ka

GATE Physics Mock Test Series - 2 - Question 4

A particle of mass m moves in a central force field defined by if E is the total energy supplied to the particle, then its speed is given by .

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 4

Given F =
so , V(r) =
Now energy, E =

GATE Physics Mock Test Series - 2 - Question 5

The space - time coordinates of two events as measured by O are x1= 6 * 104 m ,y1 = z1= Om, t1’ = 2 * 104sec and X2,= 12 x 104m, t2 = 1 x 10-4sec. What must be the velocity of O’ with respect to O if O’ measures the two events to occur simultaneously ?

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 5

Subtracting two Lorentz transformation.

On solving , we obtain,

Therefore , v is in the negative x - direction.

GATE Physics Mock Test Series - 2 - Question 6

The value of the surface integral where s is the surface of the sphere x2+ y2 + z2 = 4, n is the unit outward normal and

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 6

On putting x = x = r sinθ cosφ
y = r sinθ sinφ
z = r cosθ, we get

= π x 8

GATE Physics Mock Test Series - 2 - Question 7

Fourier series which will represents f(x) = x sinx in the interval -π< x< π, then

will have value

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 7

The given f(x) Function f(x) = xsin x is an even function. Hence series will be
f(x) = x sin x

If n =1

f(x) = x sin x

Divided each side by 2

GATE Physics Mock Test Series - 2 - Question 8

A particle moving in a central force located at r = 0 describes the spiral r = e, the magnitude of force is inversely proportional to

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

r = e

Equation of orbit

GATE Physics Mock Test Series - 2 - Question 9

Rest mass energy of an electron is 0.51 MeV. A moving electron has a kinetic energy of 9.69 MeV. The ratio of the mass of the moving electron to its rest mass is

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 9

E = mc2 - m0c2 ⇒ E =
9.69 =
10.2 =
m =

GATE Physics Mock Test Series - 2 - Question 10

A system of four particles is x - y plane. Of these, two particles each of mass m are located at (-1, 1) and (1, -1). The remaining two particles each of mass 2m are located at (1, 1) and (-1, 1). The xy component of the moment of inertia tensor of this system of particles is -

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 10

The xy component of the moment of inertia tensor

Two particles of mass m located at (-1,1) and (1, -1) other particles of mass 2m are located at (1, 1) and (-1, 1)
W = - [m1x1y1 + m2x2y2 + m3X3y3 + m4x4y4]
= - [(mx -1 x 1 ) + (m x 1 x -1 ) + (2m x 1x1) + (2m x 1x-1)]
= - [-m -m + 2m - 2m]
= [2m] ⇒ Ixy = 2m

GATE Physics Mock Test Series - 2 - Question 11

What is the energy of a uniformly charged spherical shell of total charge q and radius R.

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 11

The self energy stored in the system

Now the potential at the surface of the sphere is

GATE Physics Mock Test Series - 2 - Question 12

A current I is uniformly distributed over a wire of circular cross section, with radius a, suppose the current density in the wire is proportional to the distance from the axis J = Kx (K is constant)
Find the total current in the wire

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 12

The area - perpendicular to flow is πa2, so
J =
J varies with x. Then the current I =

GATE Physics Mock Test Series - 2 - Question 13

For a Gaussian wave packet described by The expectations value of the momentum operator is

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 13

Expectation value of the momentum operator is

< p > = 0

GATE Physics Mock Test Series - 2 - Question 14

The wave function of a particle is given by ψ= c exp (-x2α2 ) ,  co where c and a are constants. The probability of finding the particle in the region

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 14

The probability of finding the particle in the region 0 < x <  is

Now using the normalization condition

GATE Physics Mock Test Series - 2 - Question 15

A particle is moving with one component of constant velocity parallel to the axis of y and another component of velocity parallel to the axis of x proportional to y. It will describe a

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 15

When a body is moving parallel to the axis of y and moving parallel to x-axis then it's intersecting point is like a parabola .

GATE Physics Mock Test Series - 2 - Question 16

The solution of the differential equation for subject to the initial condition y(O) = 0 and ,is

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 16

The differential equation is ,
complementary function (C.F) =
(D2 - 1 ) y = 0 , so D = ±1
C.F. =
Now particular integral PI =

Complete solution of given differential equation is
Apply boundary conditions, y(0) and
At t = 0 , y = 0 , we have y(0) = A + B
At t = 0 , we have

from those equations A = 0 , B = 0
y(t) = t sin ht

GATE Physics Mock Test Series - 2 - Question 17

A nozzle in the shape of a trun cated cone, as shown in the figure. The area at the wide end is 25 cm2 and and the narrow end has an area of 1 cm2, water enters the wider end at a rate of 500 gm/sec the height of the nozzle is 50 cm and it is kept vertical with the wider end at the bottom. The magnitude of the pressure difference in k Pa between the two ends of the nozzle is

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 17

According to Bernoulli’s equation

Now given that θ = 500 gm / sec

According to equation of continuity

GATE Physics Mock Test Series - 2 - Question 18

What is the magnitude of the linear momentum of a photon of radiation having electric field described by e =

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 18

The equation for the electric field of an electro- magnetic wave can be written as

GATE Physics Mock Test Series - 2 - Question 19

Given that the magnetic flux through the closed loop PQRSP is  along PQR, the value of  along PSR is

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 19

Consider the closed loop PQRS as shown in the figure

It is given that

GATE Physics Mock Test Series - 2 - Question 20

Two infinitely extended homogeneous isotropic dielectric media (medium - 1 and medium - 2 with dielectric constant  respectively) meet at the z = 0 plane as shown in the figure. A uniform electric field is given by  The interface separating the two media is charge free. The electric displacement vector in the medium 2 is given by

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 20

Given that

And the interface separating of the two media is charge free.
Since, there is no free charge at the interface. So, normal component of  is continuous at the boundary

GATE Physics Mock Test Series - 2 - Question 21

Which of the following truth table for the given logic is true ?

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 21

At point X1
At X2 output is X2 = X + Y (OR GATE)

So, Z = X1 +X2(OR GATE)

GATE Physics Mock Test Series - 2 - Question 22

Magnetic flux linked with a stationary loop of resistance R varies with respect to time during the time period T as follows:

Find the amount of heat generated in the loop during that time. Inductance of the coil is negligible

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 22

Given that =  at(T - 1)
Induced e.m.f.e =
= dt (0 - 1) + a (T - 1)
= a (T - 2t)
So induced e.m.f. is also a function of time.
∴  Heat enerated in time T is

GATE Physics Mock Test Series - 2 - Question 23

At t = 0, a particle of mass m having v0 starts moving through a liquid kept in a horizontal tube and experiences a drag force  It covers a distance L before coming to rest. If the times taken to cover the distances  are t2 and t4, respectively, then

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 23

By Applying the second law of motion

The characterstic equation is

General solution

using the condition
C+ c2 = 0

using the condition V(0) = V0

using equations → x(t)

from the question

GATE Physics Mock Test Series - 2 - Question 24

The simplified logic expression for the following logic diagram is

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 24

GATE Physics Mock Test Series - 2 - Question 25

For the logic circuit shown in the figure, the output y is given by

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 25

So, y =
By dinorgen theorem

GATE Physics Mock Test Series - 2 - Question 26

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 200 H2 then the fundamental frequency of the open pipe - The fundamental frequency of the open pipe is

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 26

Length of the organ pipe is same in both the cases, fundamental frequency of open pipe is  and frequency of third harmonic of closed pipe will be
Given that f2 = f1+ 200

GATE Physics Mock Test Series - 2 - Question 27

A paint particle of mass M attached to one end of a massless rigid non - conducting rod of length L. Another paint particle of the same mass is attached to the other end of the rod. The two particles carry changes + q and -q respectively. This arrangement is held in a region of a uniform electric field E such that the rod makes a small angle  with the field direction. Find the minimum time needed for the rod to become parallel to the field after it is set free

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 27

A torque will act on the rod, which tries to align the rod in the direction of electric field. This torque will be of restoring nature and has a magnitude PE sinθ. Therefore

since θ is very small so that sin θ Sin θ ≈ θ

As α is proportional to - θ, motion of the rod is s impleharmonic in natural time period of which is given by

the desired time will be

GATE Physics Mock Test Series - 2 - Question 28

Which of the following statement regarding the electric fields  is correct

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 28

Only   field can represent electrostatic field..

GATE Physics Mock Test Series - 2 - Question 29

A system of four identical distinguishable particles has energy  The single particle states are available at energies   Find the average number n(E) of particles in energy e =

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 29

The possible distribution which can give a total energy are shown in table

GATE Physics Mock Test Series - 2 - Question 30

Consider 10 atoms fixed at lattices sites. Each atom can have magnetic moment   in the z - direction. Let f (μ) denote the probability that the magnetic moment of the system is μ. Assuming statistical mechanics to hold. Find the value of

Detailed Solution for GATE Physics Mock Test Series - 2 - Question 30

The magnetic moment can be  if 6 atoms in state and 4 in  state. This can happen in n

for magnetic moment to be zero , five atoms should be in state and five in state. This can happen in n2 ways where

The probability will be proportional to the no. of microstates. Hence

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