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GATE Physics Mock Test Series - 4 - Physics


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60 Questions MCQ Test GATE Physics Mock Test Series - GATE Physics Mock Test Series - 4

GATE Physics Mock Test Series - 4 for Physics 2023 is part of GATE Physics Mock Test Series 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 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for GATE Physics Mock Test Series - 4 below.
Solutions of GATE Physics Mock Test Series - 4 questions in English are available as part of our GATE Physics Mock Test Series for Physics & GATE Physics Mock Test Series - 4 solutions in Hindi for GATE Physics Mock Test Series course. Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free. Attempt GATE Physics Mock Test Series - 4 | 60 questions in 180 minutes | Mock test for Physics preparation | Free important questions MCQ to study GATE Physics Mock Test Series for Physics Exam | Download free PDF with solutions
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GATE Physics Mock Test Series - 4 - Question 1
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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
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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,

GATE Physics Mock Test Series - 4 - Question 3
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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
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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
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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
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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 = 3.58 cal/K.

GATE Physics Mock Test Series - 4 - Question 7
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 g 
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
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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
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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 = 

*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 31
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For the given differential form y3z3dx + 2xyz3dy + 3xy2z2dz Which of following are correct ?
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 31

The given differential form can be written as



is conservative
can be written as gradient of some scalar function 


*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 32
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Which of the following statements is/are correct ?
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 32

For Hermitian matrix 


For anti Hermitian 


*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 33
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The electron in a hydrogen atom makes a transition n1→ n2 where n1 and n2 are the principle quantum numbers of two states.Assume the bohr model to be valid. The time period of the electron in the initial state is twenty seven times that in the final state. The possible value of n1 and n2 are
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 33

Time period 


*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 34
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During the melting of a slab of ice at atmospheric pressure :
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 34

There is a decrease in volume during melting of an ice slab at 273 K. Therefore, negative work is done by ice water system on the atmosphere or positive work done on the ice - water system by the atmosphere.
Secondly heat is absorbed during melting (dQ is positive) and as we have seen, work done by ice water system is negative (dω is negative). Therefore from first law of thermodynamics 
du = dQ - dω
change in internal energy of ice water system, du will be positive or internal energy will increases.

*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 35
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A particle is moving in two - dimensional potential well 
V(x, y) = 0         0 ≤ x ≤ L , 0 ≤ y ≤ 3L
= ∞           elsewhere
Which of the following statement about the ground state energy E1 and ground state eigenfunction φ0 are true ?
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 35

We know In two dimensional box

And the eigen function

For normalization

*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 36
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Consider a simple harmonic oscillator made up of a mass attached to a spring. What will not be the effect in the motion if the mass were to stay completely immersed in a liquid?
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 36

Magnetic field at centre B =
Since, a compass makes 45° to the plane of coil.
So, earth magnetic field = magnetic field due to coil = 23.55 μT
 

*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 37
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A circular coil of radius 120 mm with 10 turns is placed with its plane parallel to the earth’s magnetic field. When a current of 0.45 A flows through the coil, a compass needle placed at the centre of the coil is seen to be deflected by an angle of 45° to the plane of the coil. Assign the correct statements.
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 37

The motion is simple harmonic but with a frequency which is lower compared to when it is in air, the motion is always of the damped harmonic type and always overdamped.

*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 38
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Consider a region of space in which there are uniform electric and magnetic fields which are mutually parallel. A charged particle released from rest in this region. Then which paths are impossible for this particle.
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 38

Electric field will accelerate the charge in the direction of E. 
Since, velocity of charge is parallel to B.
So, Lorentz force F = 
So, charged particle move in straight line.

*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 39
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Consider the following truth table.

The logic expression for F is
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 39




*Multiple options can be correct
GATE Physics Mock Test Series - 4 - Question 40
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In an npn transistor, 95% of emitted electrons reach the collector. If the collector current is 19 mA. Then
Detailed Solution for GATE Physics Mock Test Series - 4 - Question 40



GATE Physics Mock Test Series - 4 - Question 41
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The power radiated by sun is 7.6 x 1026 W and its radius is 7x 105 km. The magnitude of the Poynting vector (in W /cm2) at the surface of the sun is _____ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 41

We know that
The poynting vector =

= 12349

GATE Physics Mock Test Series - 4 - Question 42
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A particle is in a state which is a superposition of the ground state ψ0 and the second excited state ψ2 of one - dimensional quantum harmonic oscillator. The state is given by  . The expectation value of the energy of the particle in this state (in unit of  ____________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 42

We know that
In one dimensional harmonic oscillator

The expectation value of the energy is

GATE Physics Mock Test Series - 4 - Question 43
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A rod is moving with aspeed of 0.6c in a direction at 30° to its own length . The percentage contraction in the length of the rod is ________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 43

We know observed length in moving frame



GATE Physics Mock Test Series - 4 - Question 44
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X - rays of wavelength 0.28 nm are compton scattered and the scattered beam is observed at an angle of 60° relative to incident beam . The compton wavelength of the electron is 0.00243 nm. The kinetic energy of scattered electrons in eV is ______.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 44

19 to 20


= 28 nm + 0.001215 = 28.001215 nm

GATE Physics Mock Test Series - 4 - Question 45
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An iceberg is floating in sea water. The density of ice is 0.92 gm/cm3 and that of sea water is 1.03 g/cm3. What percentage of the iceberg will be below the surface o f water ______ %.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 45

For the floating of ice - berg
weight of ice = upthrust due to displaced water

GATE Physics Mock Test Series - 4 - Question 46
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A 5 kg block is kept on a horizontal platform at rest. At time t = 0, the platform starts moving with a constant acceleration of 1 m /sec2. The coefficient of friction μ between the block and the platform is 0.2. The work done by the force of friction on the block in the fixed reference frame in 10 sec is _______ J.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 46

Assuming that the block does not slide on the platform 
Ff = ma = 5 x 1 N 
N - mg = 0 ⇒ N = mg = 50 N

The block will remain at rest relative to the platform
Displacement D relative to the ground = 
work done by force of friction on the block = F.d = 250 J

GATE Physics Mock Test Series - 4 - Question 47
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The temperature difference between hot TA and cold Tc reservoirs of two carnot engines A and B are same . If the ratio of the respective efficiencies  is equal to then the ratio of the hot reservoir temperature is ____________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 47


ΔT same for both A and B engines

GATE Physics Mock Test Series - 4 - Question 48
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Two insulating cylinders A and B fitted with pistons contain equal amount of an ideal diatomic gas at temperature 300 K. The piston A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30K. Then the rise in temperature of the gas in B is ________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 48

For cylinder A

For cylinder B :

For diatomic gas

GATE Physics Mock Test Series - 4 - Question 49
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The directional derivative of the function f = x2​ - y2 + 2Z2 at the point P(1, 2, 3) in the direction of line PQ where Q is the poin t (5, 0, 4 ) is ________.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 49

Here function f = x2 - y2 + 2z2 

Now vector 
unit vector in direction of 

so, directional derivative of f in the direction of

GATE Physics Mock Test Series - 4 - Question 50
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In a YDSE using light, the apparatus has two slits of unequal widths. When only slit-1 is open, the maximum observed intensity on the screen is 9I0. When only slit-2 is open the maximum observed intensity is 4I0. When the both slits are open, an interference pattern appears on the screen. The ratio o f principle maxima to that of the nearest minima is _________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 50


GATE Physics Mock Test Series - 4 - Question 51
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Two blocks are connected by a spring of spring constant K. one block has K 2mass 2m and the other block has 3m. If the ratio  = 8sec-2 , the angular m frequency of vibration ω of the two block spring system in sec-1 is ________.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 51

Given that 
Reduced mass 
angular frequency 

GATE Physics Mock Test Series - 4 - Question 52
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The total power emitted by a spherical black body of radius R at a temperature T is P1. Let P2 be the total power emitted another spherical black body of Radius 2R kept at temperature T/2. The ratio  is_________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 52

We know that
For a spherical black body

GATE Physics Mock Test Series - 4 - Question 53
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The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current I is m. If this loop is changed to a circular shape with the same current I passing through it, the magnetic dipole moment becomes nm. The value of n is _______ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 53

Let the side of a square is a. 
then the magnetic moment m = La2
Now, magnetic dipole moment associated with the circular shaped loop 
carrying current I is m' = LπR2 
given that 2πR = 4a

GATE Physics Mock Test Series - 4 - Question 54
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A particle of rest mass M is moving along the positive x-direction. It decays into two photons y1 and y2 as shown in the figure. The energy of y1 is 1 GeV GeV and the energy of y2 = 0.84 GeV. The value of M (in units of ) is __________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 54

The total energy of particle of mass M = Total energy of photons.

__________(1)


GATE Physics Mock Test Series - 4 - Question 55
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Two particles of identical mass move in circular orbits under a central potential . Let  be the angular momenta and r1 , r2 be the radii of the orbits respectively. If = 2, the value r1/r2 is___________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 55

We know that central force is conservative in central potential field

In circular orbit

Ratio of angular momentum 

squaring both sides, we have 

GATE Physics Mock Test Series - 4 - Question 56
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The minimum energy of an electron (the rest mass of which is 0.5 MeV) that can emit Cerenkov radiation while passing through water (of refractive index 1.5) is approximately in MeV_________.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 56

The minimum energy of an electron is



GATE Physics Mock Test Series - 4 - Question 57
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A binary star system consists of two stars S1 and S2 with masses m and 2m respectively separated by a distance r. If both S1 and S2 individually follow circular orbits around the centre of mass with instantaneous speeds V, and V2 respectively the speeds ratio V1/ V2 is____________ .

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 57

Since the stars are moving in a circular orbit then their angular momentum must be conserved at each point.
Apply Conservation of angular momentum 
L1 = L2
m V1 r = 2m V2 r
Hence ; here , the radius of circle remains Same in both cases.

GATE Physics Mock Test Series - 4 - Question 58
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The minimum energy of a collection of 6 non-interacting electrons of spin  and mass m placed in a one dimensional infinite square well potential of width L is _________.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 58

Total energy 
ET = 2E1 + 2E2 + 2E3 
E1 →ground state energy 
E2 → first excited energy 
E3 → second excited energy

GATE Physics Mock Test Series - 4 - Question 59
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The Zener diode, as shown in the figure below, has zener voltage Vz= 15V and power rating of 0.5 W If Vs = 40 V. Find the minimum value of Rs in Ω that prevents the zener diode from being destroyed.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 59

Maximum Zones Current

minimum value of

GATE Physics Mock Test Series - 4 - Question 60
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Assume that the transistor shown in the figure is biased in the active region. Calculate the value of VCE.

Detailed Solution for GATE Physics Mock Test Series - 4 - Question 60

Let us draw its Thevenin equivalant






Applying kirchhoff law to collector circuit


= 10 -0.945 x 4 = 6.22 V

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