GATE Physics Mock Test Series - 6 - Physics MCQ

# GATE Physics Mock Test Series - 6 - Physics MCQ

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## 30 Questions MCQ Test GATE Physics Mock Test Series 2025 - GATE Physics Mock Test Series - 6

GATE Physics Mock Test Series - 6 for Physics 2024 is part of GATE Physics Mock Test Series 2025 preparation. The GATE Physics Mock Test Series - 6 questions and answers have been prepared according to the Physics exam syllabus.The GATE Physics Mock Test Series - 6 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 - 6 below.
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GATE Physics Mock Test Series - 6 - Question 1

### The energy density and pressure of aphoton gas are given by  and P = where T is the temperature and σ is the radiation constant. The entropy per unit volume is given by

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 1

According to thermodynamic equation
Tds = du + pdv

GATE Physics Mock Test Series - 6 - Question 2

### Let ψ0 and ψ2. denote respectively the ground state and second excited state energy eigenfunction of a particle moving in a harmonic oscillator potential with frequency ψ. If at time t the particle has the wavefunction, The expectation value of the energy as a function of time

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

The expectation value of an operator that does not depend on the time and commutes with the Hamiltonian is constant in time. So, (E) will remain constant with time.

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GATE Physics Mock Test Series - 6 - Question 3

### The wave function of a certain particle is  than the value of A is

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 3

GATE Physics Mock Test Series - 6 - Question 4

At constant temperature on increasing the pressure of a gas by 10% will decrease its volume by

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

If P1= Pthen P2= P + 10% of P = 1.10 P
From boyle’s lawPV = constant

∴ Percentage change in volume

GATE Physics Mock Test Series - 6 - Question 5

The independent solutions of the equation  = cos hx are —

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 5

The auxiliary equation is
m2- 3m + 2 = 0
(m - 1)(m - 2) = 0   ⇒ m = 1, 2
CF = C1ex + C2e2x

GATE Physics Mock Test Series - 6 - Question 6

Figure (A) and (B) represent respectively

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

So, (a) is AND gate

So (B) is OR GATE

GATE Physics Mock Test Series - 6 - Question 7

A U-shaped tube contains a liquid of density ρ and it is rotated about the line as shown in the figure. The difference in the levels of liquid column is

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 7

For a circular motion of small element dx

GATE Physics Mock Test Series - 6 - Question 8

The first ball of mass m moving with the velocity v collides head on with the second ball of mass m at rest. If the coefficient of restitution is e, then the ratio of the velocities of the first and the second ball after the collision is

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

Here, m1= m2 = m, u1 = u, u2 = 0. Let v1, v2 be their velocities after collision.
According to principle of conservation of linear momentum,
mu + 0 = m (v1 + v2) or v1 + v2 = u ... (i)
By definition, ....(ii)
Subtract (ii) from (i)

GATE Physics Mock Test Series - 6 - Question 9

One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 9

ΔS = 0

GATE Physics Mock Test Series - 6 - Question 10

A charge q is placed at the centre of the line joining two equal charges Q. The system of three charges will be in equilibrium if q =

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 10

Let two equal charges Q each, be held at A and B, where AB = 2x. C is the centre of AB. where charge q is held.

For the three charges to be in equilibrium, net force on each charge must be zero.
Now, total force on Q at B is

which was to be proved.

GATE Physics Mock Test Series - 6 - Question 11

At a given point in space the total light wave is composed of three phases

The intensity of light at this point is

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 11

We know intensity I = Es

GATE Physics Mock Test Series - 6 - Question 12

A radioactive sample S1 having an activity of 5μCi has twice the number of nuclei as another sample S2 which has an activity of 10μCi. The half lives of S1 and S2 can be

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 12

Activity of S1 =  (Activity of S2)

Given N1 = 2N2

GATE Physics Mock Test Series - 6 - Question 13

When a plane polarised light is normally incident on half wave plate with an angle 30° to optical axis the output light is

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 13

When a plane-polarised light is incident on half wave plate with angle θ = 30° then output emerging light is also plane polarised and making angle 2θ = 60°

GATE Physics Mock Test Series - 6 - Question 14

When plane polarized light wave is incident on a quarter wave plate at θ= 45° angle then what is the nature of output wave.

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 14

When plane polarised light is incident on quarter wave plate at θ = 45° then out light is circularly polarised. Because the phase difference provided by Q-W plate is and path difference is  so, output light is circularly polarised

GATE Physics Mock Test Series - 6 - Question 15

For the circuit shown in the given figure, assuming ideal diodes, the output waveform V0 will be

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 15

Voltage at OP-AMP output
V= - 1 - 5 sin cot
At
At
During ‘+’ ve cycle of the waveform, when V1 < -2V, diode D2 conducts and V0 = -2 V
During ‘-’ ve cycle, when V1 > 2V, D1 conducts and V0 = 2V.

GATE Physics Mock Test Series - 6 - Question 16

At normal temperature (0°C) and normal pressure (1.013 x 105 N/m2) when 1 gm. of water freezes, its volume increases by 0.091 cm3. What is the change in internal energy.

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 16

Heat given by 1 gm water when it freezes into ice
Q = mL= 1 gm x 80 cal / gm = 80 cal.
= 80 x 4.2 Joule = 336 Joule
The external work done against the atmosphere when its volume increases by 0.091 cm3

By the first law of thermodynamics, the change in internal energy

Here Q is taken negative because heat is given by the system.
Thus internal energy decreases by 336.0093 Joule.

GATE Physics Mock Test Series - 6 - Question 17

Two infinite parallel plates are uniformly charged. And the charge density on these plates are +σ and - σ respectively. The intensity of electric field between these plates will be

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 17

In I and III region direction of E1 and E2 are opposite to each other and In magnitude

So , in I and III region direction of E1 and E2 are opposite to each other and in magnitude

So, in I and III region resultant electric field is zero. But in region IInd i.e. region between plates

GATE Physics Mock Test Series - 6 - Question 18

A conductor is placed in a variable electric field . The ratio of displacement current density to conduction current density is (σ is conductivity)

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 18

Given E = E0 cosωt
Displacement vector

So displacement current density

Conduction current density

GATE Physics Mock Test Series - 6 - Question 19

For the circuit shown, which one of the following statement is true?

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 19

When S3 is closed, due to attraction with opposite charge, no flow of charge takes place through S3. Therefore, potential difference across capacitor plates remains unchanged or V1= 25 V and V2 = 15 V

GATE Physics Mock Test Series - 6 - Question 20

The internal energy of an ideal gas decreases by the same amount as the work done by the system

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 20

When loss in internal energy = work done by the system, dQ = 0, process must be adiabatic
Further, loss in internal energy indicates decrease in temp. of the gas.

GATE Physics Mock Test Series - 6 - Question 21

What is the gain V0/Vi of the circuit of figure

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 21

Applying KCL at various nodes, we have

or Vin + V2 = 2V1 = 0    (as inverting terminal is at virtual ground)
So Vin = -V2

or V3 = 3V2 = -3Vin    .....(2)

Putting values from equation (1) and (2), we get

GATE Physics Mock Test Series - 6 - Question 22

In a crystal whose primitives are 1.2A° 1.8A° and 2A°, along whose miller indices are (2, 3, 1) cuts intercept 1.2 A° along X - axis. What will be the length of intercepts along y and z - axes.

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 22

Let p, q and r be the intercepts on X, Y, and Z axes respectively, then

where a, b and c are primitives and h, k and l Miller indices.
Given that a= 1.2 Å, b = 1.8 Å and c = 2.0Å and h = 2 , k = 3 and l = 1
∴
= 0.6 : 0.6 : 2.0
As       p = 1.2 Å
∴      1.2 : q = 0.6 : 0.6
or
Similarly,     1.2 : r = 0.6 : 2.0
or
Thus the intercepts along Y and Z axes are 1.2 Å and 4 Å respectively.

GATE Physics Mock Test Series - 6 - Question 23

Two equal negative charges -q are fixed at points (0, -a) and (0, a) on y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will be

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 23

Here Q is stay at point (2a, 0) which is very for in x-axis (2a).

Motion is simple harmonic only if Q is released from a point not very far from the origin on x-axis. (for small oscillations) other wise motion is periodic but not simple harmonic. So here such type of motion is not simple harmonic motion.

GATE Physics Mock Test Series - 6 - Question 24

A uniform rod of length I is free to rotate in a vertical plane about a fixed horizon­tal axis through B. The rod begins rotating from rest from its unstable equilibrium position . When it has turned through an angle θ , its angular velocity ω is given as

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 24

When the rod rotates through an angle θ, the centre of gravity falls through a distance h. from ΔBG’ C,

..(1)
The decrease in P.E. is equal to the kinetic energy of rotation
..(2)
From equation (1) and (2), we get

GATE Physics Mock Test Series - 6 - Question 25

Consider the situation shown in the figure. All the surfaces are smooth and the rod has mass M what is the minimum value of F required to keep the rod in equilibrium ?

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 25

Clearly, the force will be minimum when upper end of the rod lies on the round support, we are excluding the case when rod is vertical In Figure, sinθ =

GATE Physics Mock Test Series - 6 - Question 26

A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 26

...(1)
Now, at P (first minima) path difference between the rays reaching from two edges (A and B) will be

Corresponding phase difference (φ) will be

GATE Physics Mock Test Series - 6 - Question 27

In a p-n junction diode not connected to any circuit

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 27

At junction a potential barrier/depletion layer is formed, with n-side at higher potential and p-side at lower potential. Therefore, there is an electric field at the junction directed from the n-side to p-side.

GATE Physics Mock Test Series - 6 - Question 28

A planet of mass m and angular momentum L moves in a circular orbit in a potential v(r)=  where k is a positive constant If the planet is slighthy perturbed, find angular frequency of radial oscillation.

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 28

for stable point (orbit)

Therefore radius of stable circular orbit is  Angular frequency of oscillation

GATE Physics Mock Test Series - 6 - Question 29

What is the ratio of the nearest neighbour distance to the next nearest neighbour distance in a simple cubic crystal

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 29

We know, in a simple cubic lattice all atoms are at eight comers of cubic lattice of length a.
So, In a simple cubic lattice, the distance of nearest neighbour d1 = a
and the distance of next nearest neighbour d2 = a√2

GATE Physics Mock Test Series - 6 - Question 30

What is the maximum radius of the sphere that can just fit into the void at the body centre of the fee structure coordinated by the facial atom. Given r is the radius of atom.

Detailed Solution for GATE Physics Mock Test Series - 6 - Question 30

The situation is shown in Fig. Let R be the radius of the sphere that can just fit into the void.
From figure, 4 + R = a/2
∴     R = (a/2) - r ..(1)

We know that for fee structure
a = 4r/√2 ..(2)
Substituting the value of a from eq.(2) in eq. (1), we get

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