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GATE Physics Mock Test Series - 7 - Physics MCQ


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30 Questions MCQ Test - GATE Physics Mock Test Series - 7

GATE Physics Mock Test Series - 7 for Physics 2024 is part of Physics preparation. The GATE Physics Mock Test Series - 7 questions and answers have been prepared according to the Physics exam syllabus.The GATE Physics Mock Test Series - 7 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 - 7 below.
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GATE Physics Mock Test Series - 7 - Question 1
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If an integral curve of the differential equation  = 1 passes (0.0) and (α,1), then α is equal to

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 1

Given differential equation is


So, the required solution is

y(0) = 0
0 = 0 - e° + c ⇒c = 1 
Then the solution becomes 
xey = yey - ey + 1
y(α)=1
αe = e - e+1
α = e-1

GATE Physics Mock Test Series - 7 - Question 2
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The potential φ in Joule of a particle of mass 1 kg moving in x - y plane obey the law of φ = 3x + 4y. Here x and y are in meters. If the particle is at rest at (6m, 8m) at time t = 0, then the work done by conservative force on the particle from the initial position to the instant when it crosses the x - axis is

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


OR, the direction of motion of the particle is along the origin. The particle will cross the X-axis at origin.
So, by the energy conservation at time t = 0, (6m, 8m) and at origin 
Ki+ Ui = Kf + Uf
0 + ( 6 x 3 + 4 x 8 ) = K f + ( 0 x 3 + 0 x 4 )

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GATE Physics Mock Test Series - 7 - Question 3
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A solid uniform disc of mass m rolls without slipping down a fixed inclined plank with an acceleration α. The frictional force on the disc due to surface of the plane is

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

We know that, the angular all eleration 

and now frictional force 

GATE Physics Mock Test Series - 7 - Question 4
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Consider the earth as a uniform sphere of mass M and radius R. Imagine a straight smooth tunnel made through the earth which connects any two points on its surface. The motion of a particle of mass m along this tunnel under the action of gravitation simple harmonic. Determine the time that a particle would take to go from one end to the other through the tunnel.
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 4


Suppose at some instant the particle is at radial distance r from centre of earth O. since the particle is constrained to move along the tunnel, we define its position as distance x from c. Hence, equation of motion of the particle is max = fx
The gravitational force on mass m at distance r is F = 
Therefore,

Since, Fx α- x , motion is simple harmonic in nature. 

Time period of oscillation  
Hence, the time taken by the particle to go from one end to another end is

GATE Physics Mock Test Series - 7 - Question 5
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A glass plate of thickness 30 mm is placed just below a well-focused microscope for focusing it again the microscope should be moved through a distance of :
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 5

The shift is path when an obstacle of refractive index μ and of length is kept in way of a ray is given as path difference
= ( μ - 1 ) t = (1.5 - 1 ) 30 mm = 15 mm

GATE Physics Mock Test Series - 7 - Question 6
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The Clausius-clapeyron equation indicates that the increase of pressure increases the melting point.
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 6

Clausius-clapeyron equation is given as

⇒ If volume increases the pressure increases with T.

GATE Physics Mock Test Series - 7 - Question 7
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The magnitude of the de-Broglie wavelength λ of electron (e), proton (p), neutron (n) and α - particle (α) all having the some energy of 1 MeV, in the increasing order will follow which of the following sequence :
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 7

According to de-Broglie the wavelength associated with a particle of mass m moving with velocity v is given as

KE x 2m = (mv)2 
mv = √2m E

GATE Physics Mock Test Series - 7 - Question 8
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The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 8

The frequency of cyclotron f 107 Hz
for cyclotron 
mv = Bqr

frequency  
kinetic energy 

GATE Physics Mock Test Series - 7 - Question 9
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Two identical capacitors A and B shown in the given circuit are joined in series with a battery. If a dielectric slab of dielectric constant K is slipped between the plates of capacitor B and battery remain connected then the energy of capacitor A will
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 9

The energy stored in capacitor of capacity C and potential V is given as

Now when slab of dielectric constant K is introduced without disconnecting the battery the equivalent capacities becomes


∵  energy increases.

GATE Physics Mock Test Series - 7 - Question 10
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Consider a particle with three possible spin state S = 0 and ±1. There is a magnetic field h present and the energy for a spin state S is -hS. The system is at a temperature T. Which of the following statements is true about the entropy S(T) ?
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 10

we know that
Entropy s = K In Ω at high temperature T, microstates are 3. 
So, s = K In 3.
at law temp T= 0 K, microstate = 1 
(at T = 0 K; system is perfect ordered ) 
s = K In 1 = 0

GATE Physics Mock Test Series - 7 - Question 11
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Consider three situations of 6 particles in one dimensional box of width L with hard walls. In case (i), the particles are fermions, in case (ii) they are bosons and in case (iii) they are classical. If the total ground state energy of the six particles in these three cases are EF, EB and Ecl respectively, which of the following is correct ?
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 11

The energy eigenvalue, In one dimensional box is


for fermions

for Bosons

for classical 

GATE Physics Mock Test Series - 7 - Question 12
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The electric fields inside (r < R) and outside (r > R) a solid sphere with a uniform  volume charge density are given by , respectively, while the electric field outside a spherical shell with a uniform surface charge  density is given by  being the total charge. The correct ratio of the electrostatic energies for the first case to second case is
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 12

We know that
The electrostatic energy 
for the spherical shell 

for the solid sphere 

GATE Physics Mock Test Series - 7 - Question 13
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Le t   where c is the boundary (oriented anticlockwise ) of the region in the first quadrant bounded by y = 0, x2 + y2 = 1 and x = 0. The value of I is
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 13

By green’s theorem


GATE Physics Mock Test Series - 7 - Question 14
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A quantum mechanical particle in a harmonic oscillator potential has the initial wave function  , where ψ0 and ψ1 are the real wave functions in the ground and first excited state of the harmonic oscillator. For convenience we take m = ℏ = ψ= 1 for the oscillator. What is the probability density of finding the particle at x at time t = π ?
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 14


Now probability density at time t

putting t = π

GATE Physics Mock Test Series - 7 - Question 15
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A particle of mass m is thrown upward with velocity v and there is retarding air resistance proportional to the square of the velocity with proportionality constant K. If the particle attains a maximum height after time t, and g is the gravitational acceleration, what is the velocity.
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 15

Equation of motion  

GATE Physics Mock Test Series - 7 - Question 16
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A monochromatic wave propagating in a direction making an angle 30° with the y-axis in the reference frame of source. The source moves at speed v  towards the observer. The direction of the (cosine of angle) wave as seen by the observer’s _____ .
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 16


Now    

GATE Physics Mock Test Series - 7 - Question 17
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A system of two circular co-axial coils carrying equal currents i along same direction having equal radius R and separated by a distance 2R (as shown in figure below). The magnitude of magnetic field at the midpoint P is given by
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 17


Similarly

So, total magnetic field at point P is 

GATE Physics Mock Test Series - 7 - Question 18
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Consider a system of 4N non-interacting spin  particles each fixed in position and carrying a magnetic moment μ . The system is immersed in a uniform magnetic field B. The number of spin down particle for which the entropy of the system will be maximum is
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 18

Let us consider n number of spin out of 4N particle have spin down remaining 4N-n is up.
Number of ways 
Entropy 


for entropy maximum at equilibrium for spin  down particle 


GATE Physics Mock Test Series - 7 - Question 19
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The spectral emission power of a black body at 6000K is maximum at 5000˙A . If the temperature is increased by 10% then decrease in the value λm will be
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 19

According to Wein's displacement law:
λT=b
when the temperature increases by 10%
the new temperature becomes 6600K
5000˙A×6000=λ×6600
i.e. λ=4545˙A
Change in wavelength =455˙A
i.e. change in wavelength =455/5000=10%

GATE Physics Mock Test Series - 7 - Question 20
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Let be a matrix with real entries. If the sum and the product of all the eigen values of A are 10 and 30, respectively, then a2+b2 equals
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 20

Given 
Characteristic polynomial of A = t2 - tr(A)t + |A|
                                              = t2 - (a + b + 3) t + 3ab
Sum of eigen values = 10 
and product of eigen values = 30 
⇒ a + b + 3 = 10⇒ a + b = 7 
3ab = 30 ⇒ ab = 10
Now, a2 + b2 = (a + b)2 - 2ab
= (7)2-2x10 = 29

GATE Physics Mock Test Series - 7 - Question 21
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A 150Ω resister, a l0μf capacitor a 0.1 H inductor are connected in series to an AC source operating at an angular frequency ω, for what ω the combination acts as a pure resistive load.
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 21

Consider the LCR circuit of impedance

The combination acts as purely resistive circuit if

GATE Physics Mock Test Series - 7 - Question 22
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Consider two electromagnetic plane waves propagating in vacuum with their electric field vectors

then the averaged pointing vector for the resultant wave
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 22

According to the question, electric fields are

Net electric field
E = E1 + E2


Magnetic field 

GATE Physics Mock Test Series - 7 - Question 23
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A convex lens of focal length 24 cm (μ = 1.5) is totally immersed in water. Its focal length in water is _______ .
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 23


When the lens is in air

When the lens is in water

GATE Physics Mock Test Series - 7 - Question 24
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Unpoiarized light falls on two polarizing sheets placed on top of the other. What be the angle between the characteristic directions of the sheets if the intensity of the transmitted light is one third intensity of the incident beam_______ .
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 24

Intensity of light transmitted through the first polarizer 
where I0 is the intensity of the incident unpolarized light.
Intensity of the light transmitted through the second polarizer is I2 = I0 cos2 θ

GATE Physics Mock Test Series - 7 - Question 25
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What is the maximum range along the dashed line attained by the water stream coming out at B from a thin tube of the water tank assembly shown in the figure ?
Assume h = 10m, L = 2m and θ = 30°
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 25

Let V be the velocity of the water coming out from the point B. Applying conservation mechanical energy
PEA =KEB + PEB


The water ejected at point B will fallow the projective motion.

Range = 
Total Range 

Total Range 

GATE Physics Mock Test Series - 7 - Question 26
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Consider the digital circuit shown below in which the input C is always high (1)

The truth table for the circuit can be written as

The entries in the Z column (vertically) are
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 26

This is X-OR-GATE in which when both inputs are same 
then output will be zero if both inputs are not same then output will be high so for
the Ist set
(i ) A = 0, B = 0      then A . B = 0 = y1
and B = 0, C = 1    then Y2 = 1
... (a)
(ii) A = 0, B = 1 them Y1 = A . B = 0 
B = 1, C = 1   then Y2 = 0
...  (b)
(iii) A = 1, B = 0      then Y1= A .B = 0
B = 0, C = 1   then Y2 = 1
.... (c)
(iv) A = 1, B = 1   then Y1 = A . B = 1 
B = 1, C = 1     then Y2 = 0
 .....(d)
so the output is 1011

GATE Physics Mock Test Series - 7 - Question 27
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In the operational amplifier circuit below, the voltage at point A is
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 27

By the help of virtual ground’s condition then potential at A point of inverting terminal is equal to at point O of non-inverting terminal. Let potential at 0 is considered as VA then q by the help of node analysis at point 0.

GATE Physics Mock Test Series - 7 - Question 28
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In the differential mode :-
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 28

In differential mode |V1 = V2| but with opposite polarity & in common mode ( V1= V2) but with same polarity.

GATE Physics Mock Test Series - 7 - Question 29
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In the op-amp circuit shown in the figure below, the input voltage V1 is 1V. The value of the output Vo is
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 29

due to virtual grand concept V = 0 at point A

then

GATE Physics Mock Test Series - 7 - Question 30
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The output, 0, of the given circuit is cases I and II, where 
Case I : A, B = 1; C, D = 0; E, F = 1 and G = 0
Case II : A, B = 0; C, D = 0; E, F = 0 and G = 1 
are, respectively
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 30


Let o/p of AB is x, of CD is y and of x and y is z and o/p or z and E is x’ of x’ and f is y’ and o/p of y’ and G is z’. And z’ is the final output given that 
for Case I        A, B = 1 ; C,D = 0 ; E, F = 1 and G = 0 
Case II            A, B = 0 ; C,D = 0 ; E, F = 0 and G = 1 
For Case I

⇒ z = x + y = 0 + 0 = 0
y = 0.0 = 0
x’ = z. E = 0
y’ = x’ + F = 0 + 1 =1

For case II

⇒ z = x = y = 1 
y = 0.0 = 0 
x’ = Z.E= 1.0 = 0
y’ = x’ + F = 0 + 0 = 0

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