GATE Physics Mock Test Series - 3 - Physics MCQ

# GATE Physics Mock Test Series - 3 - Physics MCQ

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## 30 Questions MCQ Test GATE Physics Mock Test Series 2025 - GATE Physics Mock Test Series - 3

GATE Physics Mock Test Series - 3 for Physics 2024 is part of GATE Physics Mock Test Series 2025 preparation. The GATE Physics Mock Test Series - 3 questions and answers have been prepared according to the Physics exam syllabus.The GATE Physics Mock Test Series - 3 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 - 3 below.
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GATE Physics Mock Test Series - 3 - Question 1

### At what speed the volume of an object will shrinks to half its rest volume?

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 1

Let the volume (initial) be ‘V ’

GATE Physics Mock Test Series - 3 - Question 2

### Calculate the energy released by 1 g of natural uranium assuming 200 MeV is released in each fission event and that the fissionable isotope 235U has an abundance of 0.7% by weight in natural uranium.

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

235 gm uranium contains 6.02 x 1023 nuclei
So, in 1 gm no. of nuclei

So, total energy released = 2.56 x 1021 x 200 MeV = 5.12 x 1023 MeV
According to energy released = 5.12 x 1023 x 1.6 x 10-19 x 106 x Joule
= 5.7 x 108 J

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GATE Physics Mock Test Series - 3 - Question 3

### A charged particle of mass'm',charge 'q' and constant velocity  enters a uniform magnetic field  at an angle θ to the direction of magnetic field.The angle'θ'(if,one revolution of the helical motion,the particle advances along the direction of the magnetic field at a distance equal to the radius of the helical path) is:-

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

time taken for 1 revolution (T)=

GATE Physics Mock Test Series - 3 - Question 4

A free particle is moving in positive direction with linear momentum (p) The wave function of the particle normalized in a length (L) is:-
Applying normalization, we get

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

Applying Schrodinger’s equation :-

Solution o f this equation is
Applying boundary condition ψ(O) = 0
⇒ A sinO + B cos 0 = 0 ⇒ B = 0
Hence wave function is
Applying normalization, we get

GATE Physics Mock Test Series - 3 - Question 5

The solution of the differential equation  with the boundary condition that y = 1, at x=1 is:—

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 5

We have

solution is y .x =
but y = 1 at x = 1
solution is yx =

GATE Physics Mock Test Series - 3 - Question 6

A particle of mass 2kg is moving such that at time t second, its position in meter is given by  The angular momentum of the particle at t = 2 sec about the origin in kg m2/sec is

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

Given that

at time t = 2 sec

velocity vector

at time t = 2 sec

momentum vector
Angular momentum

GATE Physics Mock Test Series - 3 - Question 7

If z = f(x, y), where x = g(t), y = h(t), g(3) = 2, g'(3) = 5, h(3) = 7, h'(3) = -4,  fx(2, 7) = 6, fy(2,7) = -8, then the value of   at t = 3 is

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 7

z = f(x, y)

At t = 3, x = g(3) = 2, y = h(3) = 7

= fx(2, 7).g'(3) + fy(2, 7)h'(3) 6 x 5 + (-8 ) x ( - 4) = 62

GATE Physics Mock Test Series - 3 - Question 8

If  are non coplanar unit vectors such that  then the angle between is

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

We have

then

GATE Physics Mock Test Series - 3 - Question 9

A system of four particles is in x-y plane of these two particle of masses 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 moment of inertia tensor of the system of particle is

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 9

The xy component of inertia tensor is

Ixy = -[(m x1x1) + (m x-1x1) + (2m x1x-1) + 2m(-1x-1)]
= - [ m - m - 2m + 2m ]
= 0

GATE Physics Mock Test Series - 3 - Question 10

Consider circular orbits in a central force potential V(r) =  , where k > 0 and o < n < 2. If the time period of a circular orbit of radius R is T1 and that of radius 3R is T3, then  is,

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 10

Veffective =

GATE Physics Mock Test Series - 3 - Question 11

After a perfectly elastic collision of two identical balls, one of which was initially at rest, the velocities of both the balls are non zero. The angle θ between the final.
Velocities (in the lab frame) is

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 11

Angle between two particle θ1 + θ2 = 0
Applying the conservation of linear momentum

Conservation of Kinetic energy

from (i) and (ii)

GATE Physics Mock Test Series - 3 - Question 12

The escape velocity of the earth is v0. For a planet having radius 4 times and density three times that of the earth, the escape velocity will be

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 12

Escape velocity

If p becomes three times and radius becomes 4 times then Escape velocity v =

GATE Physics Mock Test Series - 3 - Question 13

A pump is used to push water of density p through a tube of constant cross- section area ‘A’ shown below. What is the value of ΔP?

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 13

Since, cross-section area at A and B is same. So, velocity of water at A and B will remain same. Let us apply Bernoulli equation at A & B.

Both equations are equal
ΔP = pgH

GATE Physics Mock Test Series - 3 - Question 14

Nearest neighbour distance in Na crystal is 1.83 A°. Density of electron in Na crystal is:-

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 14

‘Na’ has bcc structure
Nearest Neighbour distance =

Density of electrons =

GATE Physics Mock Test Series - 3 - Question 15

The electric potential due to a linear quadrupole varies inversely with distance ‘r’ as :-

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 15

The potential at the point 'P ' is v =

Q = 2qa2  → Quardrupole moment of charge distribution

thus v is inversely proportional to r3 & not r-3

GATE Physics Mock Test Series - 3 - Question 16

Calculate the collector voltage (Vc) of the transistor circuit shown in the fig be- low :-

Given

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 16

since VBE« Vcc
we can neglect VBE in comparison to Vcc.

GATE Physics Mock Test Series - 3 - Question 17

The logic circuit shown in the following figure yields the given truth table.

The gate ‘x’ in the diagram is:-

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 17

Truth table for AND is given as:-

NOT of AND i.e. NAND is given as:-

than the given gate “x” is NAND gate

GATE Physics Mock Test Series - 3 - Question 18

A metal with body centered cubic (bcc) structure shows the first (i.e. smallest angle) diffraction peak at a Bragg angle of θ = 30°. The wavelength of X-ray used is 2.1 . The volume of the primitive unit cell of the metal is (for first peak, h + k + 1 should be even)

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 18

λ = 2.1Aº for bcc →h+k+l should be even for first peak,
h = 1, k=1, l=0

GATE Physics Mock Test Series - 3 - Question 19

Consider the surface corresponding to the equation 4x2 + y2 + z = 0 .A possible unit tangent to this surface at the point (1,2,-8) is

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 19

Unit normal for the surface =

Unit normal =
So, the possible unit tangent to this surface will be
Where is tangent
According to option

GATE Physics Mock Test Series - 3 - Question 20

In the laboratory frame, two observers A and B are moving along the sides of an equilateral triangle with equal speeds C/2, as shown in the figure. The speed of B as measured by A will be ______ .

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 20

According to figure

The speed of B as measured by A

Resultant velocity u =

GATE Physics Mock Test Series - 3 - Question 21

The instantaneous electric and magnetic fields created at a distance r by a point source at the origin are given by

Where ω, A, B are constants and the unit vectors from an orthonormal set. The time averaged power radiated by the source is .

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 21

Given that

Pointing vector (Energy per unit time per unit area)

We know that

=> The time averaged power radiated by the source is = <S>. A = AB C2

GATE Physics Mock Test Series - 3 - Question 22

Electric field component of an electromagnetic radiation varies with time as E = , where a is a constant and the values of the ω and ω0 are 2 x 1015 sec-1 and 1 x 1016 sec-1 respectively. This radiation falls on a metal of work function 4.4eV. The maximum kinetic energy (in eV) of photoelectrons is

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 22

The maximum frequency of photon =

GATE Physics Mock Test Series - 3 - Question 23

If E1 is the energy of the electron in the six fold degenerative energy state (1,2,3) in a cubical potential box of side a and E2 is the energy of a particle of mass twice that of electron in the second non-degenerative energy state of a side then E2-E1

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 23

For cubical box , the eigen values of energy

E1→ state (1 ,2 ,3 ), when  side of cubical box is ‘a’ .

Now for the E2 [ in non -degeneratic state (2,2,2)] mass is twice and  side of
cubical box is

GATE Physics Mock Test Series - 3 - Question 24

Three polarisers P,Q and R are placed parallel to each with their planes perpendicular to the z-axis. Q is placed between P and R Initially, the polarising directions of P and Q are parallel but that of R is perpendicular to them . In this arrangement when unpolarised light of density l0 is incident on P , the R intensity coming out of R is zero, the polariser Q is now rotated about the z-axis. The maximum intensity of light coming out of R is

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 24

Consider three polarisers P,Q and R Initially, polarising direction of P and Q are parallel but that of R is perpendicular to them.
Intensity of light passing through P is

Intensity of light passing through Q , according to law of malus IQ = Ipcos2 φ) Intensity of light coming out of R is

sin2 φ = l( IR will be maximum , when φ= π/4)

GATE Physics Mock Test Series - 3 - Question 25

A diffraction grating having N slits , each of width b and period d , is illuminated normally by a monochromatic plane wave of wavelength λ. What is the phase difference between waves from first and Nth slit in the heighest diffraction order?

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 25

Highest number of orders with grating
dsinθ = nλ

GATE Physics Mock Test Series - 3 - Question 26

The speed of sound propagating in air as a function of temperature T is given by v = αT, where , α is a constant of appropriate dimensions. Calculate the time taken for a sound wave to travel a distance L between two points A and B , If the air temperature between the points varies linearly from T1 to T2.

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 26

Given that speed of sound v = αT

taking double integrations on both sides

Putting V1= αT1 and V2= αT2

GATE Physics Mock Test Series - 3 - Question 27

The extension in a string, obeying Hooke’s law, is x. The speed of transverse wave in the stretched string is V. If the extension in the string is increased to 1.5x, the speed of transverse wave will be

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 27

From Hooke’s law
Tension in a string (T) α extension (x) and speed of sound in string

Therefore
x is increased to 1.5 times speed will increase  by times or 1.22 times.
Therefore , speed of sound in new position will be 1.22V.

GATE Physics Mock Test Series - 3 - Question 28

Two radio stations broadcast their programs at the same Amplitude A and at slightly different frequencies ω1 and ω2 respectively, where ω1 - ω2= 103Hz. A detector receives the signals from the two stations simultaneously. It can only detect signals of intensity ≥2A2. Find the time interval between successive maxima of the intensity of the signal received by the detector.

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 28

If the detector is at x = 0, the two radio waves can be represented as
y1 = A sin ω1t                 {Given that A1 = A2}
y2 = A sin ω2t
By the principle of superposition

Now we can consider that,

So , intensity will be maximum when

Therefore , time interval any two successive maxima is

GATE Physics Mock Test Series - 3 - Question 29

A thin convex lens made from crown glass  as focal length f. When it is measured in two different liquids having refractive indices   It has the focal length f1 and f2, respectively. The correct relations between the focal length is ________ .

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 29

By the lens maker’s formula

According to lens maker’s formula, when lens in the air

In case of liquid, where refractive index is
we get
focal length in first liquid

⇒ f1 = 4 f
focal length in second liquid

f2 is negative.

GATE Physics Mock Test Series - 3 - Question 30

In a YDSE bi-chromatic light of wavelength 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distances between the plane of the slits and the screen is 1m. The minimum distance between two successive regions of complete darkness is _______

Detailed Solution for GATE Physics Mock Test Series - 3 - Question 30

Let nth minima of 400 nm coincides with mth minima of 560 nm, then

4th minima of 400 nm coincides with 3rd minima of 560 nm.
Location of this minima is

Next 11th minima of 400nm will coincide with 8 minima of 560 nm
Location of this minima is

∴      Required distance = y2 - y1 =28

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