GATE Physics Mock Test Series - 4 - Physics MCQ

# GATE Physics Mock Test Series - 4 - Physics MCQ

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## 30 Questions MCQ Test GATE Physics Mock Test Series 2025 - GATE Physics Mock Test Series - 4

GATE Physics Mock Test Series - 4 for Physics 2024 is part of GATE Physics Mock Test Series 2025 preparation. The GATE Physics Mock Test Series - 4 questions and answers have been prepared according to the Physics exam syllabus.The GATE Physics Mock Test Series - 4 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 - 4 below.
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GATE Physics Mock Test Series - 4 - Question 1

### The differential equation    satisfying y(0) = 1, y(π) = 0 has

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 1

y = c1 sinx + c2 cos x
y(0) = 1 ⇒ c1 = 1
y(π) = 0 ⇒ c2 = 0

GATE Physics Mock Test Series - 4 - Question 2

### If S is the surface (x- 1)2 + (y - 2)2 + (z - 3)2 = 1 enclosing volume V, and  , then the value of integral  is equal to

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

V is volume enclosed by surface S, given by
( x - 1 ) 2 + (y- 2 )2 + (z- 3 )2 = 1

volume of sphere of radius “1m”
Thus,

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GATE Physics Mock Test Series - 4 - Question 3

### The eigenvalues of the matrix are

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 3

The given matrix is
A2 = 1
A2 - 1 = 0
(A - 1 ) (A + 1) = 0
So, the eigenvalues of A can be either +1 or -1 .Also, trace is zero. So, the sum of eigen values is zero. So, eigenvalues are + 1, + 1.

GATE Physics Mock Test Series - 4 - Question 4

The expectation value of energy when the state of the harmonic oscillator is described by the following wave function

where ψ0(x,t) and ψ2(x,t) are wave functions for the ground state and second excited state respectively :-

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

As we know that for the Harmonic oscillator

then the expectation value of energy is

GATE Physics Mock Test Series - 4 - Question 5

While using second latent heat equation  , the specific heat of steam is negative in the following condition :-

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 5

L = 800-0.705 T

Boiling point of water
T = 100 + 273 = 373
L = 800 -0.705x373 = 537
specific heat of water
c1 = 1

c2 = -1.14

GATE Physics Mock Test Series - 4 - Question 6

For silver, the specific heat at constant pressure in the range of 50 K to 100 K is given by Cp = 0.076 T - 0.00026 T2 - 0.15 cal mol-1 deg-1 where T is the kelvin temperature. If 2 mole of silver are heated from 50 K to 100 K. Calculate the change in entropy

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 6

The change in entropy is

ds = 5.49 cal/K.

GATE Physics Mock Test Series - 4 - Question 7

A particle describes a circular orbit under the influence of an attractive central force directed toward a point at the center. The force inversely proportional to

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 7

The path equation of a circular orbit
For attractive central force

GATE Physics Mock Test Series - 4 - Question 8

An astronaut moves in a super spaceship travelling at a speed of 0.64C. The astronaut observes a photon approaching him from space. The speed of photon with respect to the astronaut i s ________ .

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

Speed of photon = c
The speed of astronaut = 0.64 c
Let the photon and astronaut super spaceship moving along positive and negative directions of x- axis respectively. Let the electron moving with velocity - 0.64c

GATE Physics Mock Test Series - 4 - Question 9

Half life of a radioactive materials is 4 days. After 20 days, the fraction remaining undecayed will be -

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 9

We ,know that

GATE Physics Mock Test Series - 4 - Question 10

After being hit, a golf ball reaches a maximum height 60 m with a speed of 30 m / sec. Right after being hit, the speed of the ball is (take g = 10 m/sec2)

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 10

GATE Physics Mock Test Series - 4 - Question 11

The vector field  in cylindrical polar coordinates is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 11

In cylindrical polar coordinate

vector,

GATE Physics Mock Test Series - 4 - Question 12

One mole of monoatomic ideal gas is initially at pressure P0 and volume V0. The gas then undergoes a three - stage cycle consisting of the following processes:
(A) An isothermal expansion till it reaches volume 2 V0 and heat Q flows into the gas.
(B) An isobaric compression back to the original volume V0
(C) An isochoric increase in pressure till the original pressure P0 is regained. The efficiency of this cycle can be expressed as

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 12

(A) Isothermal process
W = 2.303 RT log
W = 2.303 RT log 2
ΔU = 0
Q = W
(B) Isobaric process

(C) Isochoric process
ΔW =0

Total heat absorbed by the system

Total Work done W =
efficiency

GATE Physics Mock Test Series - 4 - Question 13

The normalized wave function of a particle can be written as

Where (x) are the normalized energy eigenfunction of a given Hamiltonian. The value of N is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 13

Given that

GATE Physics Mock Test Series - 4 - Question 14

The commutator of two matrices A and B are defined as
[A, B] = AB - BA
{A, B} = AB + BA
If [A,B] = 0. We can write [A,B,C] =

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 14

Given that
[A,B] = 0 ⇒ AB - BA = 0⇒ AB = BA
[ABC] = [A,B] C + B [A,C] = ABC - BAC + BAC - BCA
[A,BC] = ABC - BCA
[A, BC] = BAC = BCA = B (AC - CA)
[ABC] = B[A,C]

GATE Physics Mock Test Series - 4 - Question 15

A Solid cylinder of height H, radius R and density P, floats vertically on the surface of a liquid of densitypThe cylinder will be set into oscillatory motion when a small instantaneous downward force is applied. The frequency of oscillation is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 15

When the cylinder is pressed into the water then buoyant force will oppose its motion and sets the cylinder into simple harmonic motion.
Buoyant force = Weight of the liquid displaced by the body
= mass of water displaced x gravity
m ’g = P 0 A g x
where x is height and m’ = density x volume
m ’g = P 0 Ax
f = P 0g Ax

GATE Physics Mock Test Series - 4 - Question 16

Consider a hollow charged shell of inner radius a and outer radius b. The volume charge density is  (K is constant) in the region a < r < b. The magnitude of the electric field produced at distance r > a is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 16

Given that, a hollow charged shell of inner radius a and outer radius b.
The volume charge density is.
Where, K is a constant
Consider first surface and applying Gaussian law  zero because there is no charge density.
Hence, E = 0 for r < a
Considering second surface in the region a < r < b.

or the region a < r < b for Gaussian r > b
total charge enclosed by surface is

Applying Gaussian law

for the region r > b

GATE Physics Mock Test Series - 4 - Question 17

The wave function of a state of the hydrogen atom is given by  where , denotes the normalized eigenfunction in the usual notation. The expectation value of Lz in the state

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 17

The wavefunction of a state of the hydrogen atom is given by

where A is normalisation constant
By the normalisation condition

The normalised wavefunction

GATE Physics Mock Test Series - 4 - Question 18

A planet of mass m moves in the gravitational field of the sun (mass M). If the semi-major and semi-minor axis of the orbit are a and b respectively. The angular momentum of the planet is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 18

The effective potential in the presence of the gravitational field is given by

Where , V ( r ) is the central potential and L is angular momentum.

Applying Conservation of energy

GATE Physics Mock Test Series - 4 - Question 19

Consider an infinite conducting sheet in the xy-plan with a time dependent current density kt  where K is a constant. The vector potential at (x,y,z) is given by   The magnetic field  is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 19

The vector potential at the point (x,y,z) is given by

We know

GATE Physics Mock Test Series - 4 - Question 20

Water is flowing through a tube as shown. The cross section area at A & C are equal and greater than the cross-sectional area at B. If the flow is steady, then the pressure on the walls at B is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 20

using Bernoulli equation

from question

Now, using continuity equation AV = constant cross-sectional area o f A > B. Hence VB > VA

Similarly for region C, Pc > PB

GATE Physics Mock Test Series - 4 - Question 21

A gas of N non-interacting particles is in thermal equilibrium at temperature T. Each particle can be in any of the possible non-degenerate states of energy . The average energy per particle of the gas, when  <<< 1, is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 21

The partition function for this system is

The average energy per particle of the gas is

Now, for given condition  then

GATE Physics Mock Test Series - 4 - Question 22

A plane electromagnetic wave is propagating in a lossless dielectric. The electric field is given by

where c is the speed of light in vacuum, E0, A, and Ko, are constants and and are unit vectors along the x-axis and z-axis
The relative dielectric constant of the medium  and the constant A are

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 22

Electromagnetic wave is always transverse in nature.

The phase velocity is

Now, refractive index is defined as
But So , the relative dielectric constant of the medium

GATE Physics Mock Test Series - 4 - Question 23

A plane polarized electromagnetic wave in free space at time t = 0 is given  The magnetic field  is given by

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 23

The plane polarized electromagnetic wave in free space at time t = 0 is given by

Wave vector
The phase velocity of wave in free space is

Let electric field after time t is

using maxwell relation

GATE Physics Mock Test Series - 4 - Question 24

A circular loop of mass M and radius a rolls without slipping with constant angular speed ω along the horizontal x-axis in the x-y plane. When the centre of the hoop is at a distance d =   from the origin, the magnitude of the total angular momentum of the loop about the origin is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 24

Angular momentum is given by

GATE Physics Mock Test Series - 4 - Question 25

A particle is incident with a constant energy E on a one dimensional potential barrier as shown in the figure. The wave function in regions I and II are respectively

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 25

Schrodinger equation in region I is

The wave function in region I is is oscillatory
Schrodinger equation in region II is

When  then and this wavefunction in region II is decaying.

GATE Physics Mock Test Series - 4 - Question 26

The frequency response curve of a damped forced oscillator will be of the form (R-amplitude and VR- frequency ratio) :

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 26

The differential equation of forced oscillation is given as

solving this the amplitude is given as

The curve given for this amplitude is given as

GATE Physics Mock Test Series - 4 - Question 27

A voltage applied to an X-Ray tube being increased η = 1.5 times, the shortwave limit of an X-Ray continuous spectrum shifts by Δλ = 26 pm. Find the initial voltage applied to the tube.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 27

The general formula is

GATE Physics Mock Test Series - 4 - Question 28

Metallic copper is know to form cubic crystals and the lattice constant is measured from X-ray diffraction studies to be about 0.36 nm. If the specific gravity of copper is 8.96 and its atomic weight is 63.5, one can conclude that

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 28

Atomic weight of copper = 63.5
mass of one copper atom =
= 1.054 x 10-22
Volume of unit cell V = a3
=(0.36x10-7)3 cm3
= 4.6656 x 10-23 cm3
mass of one unit cell = 4.6656 x 10-23 x 8.96
= 4.18x10-22 g
Number of Cu atom in one unit cell

= 3.96= 4 So, crystal is f.c.c.

GATE Physics Mock Test Series - 4 - Question 29

In a simple cubic structure of lattice constant a, one plane among a set of parallel planes intercepts x,y, and z- axis 2a, a and a respectively. The interplanar spacing is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 29

Intercepts = 2a, a, a
dividing by lattice constant a, 2,1,1
Taking reciprocal  , 1,1
multiplying by 2 (1,2,2)
Miller indices is (1,2,2)
Interplanar spacing

GATE Physics Mock Test Series - 4 - Question 30

Consider a doped semiconductor having the electron and the hole mobilities μn and μp respectively. Its intrinsic carrier density is ni The hole concentration p for which the conductivity is minimum at a given temperature is

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 30

⇒ p =

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