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GATE Physics Mock Test Series - 7 - Physics


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

GATE Physics Mock Test Series - 7 for Physics 2023 is part of GATE Physics Mock Test Series 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 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for GATE Physics Mock Test Series - 7 below.
Solutions of GATE Physics Mock Test Series - 7 questions in English are available as part of our GATE Physics Mock Test Series for Physics & GATE Physics Mock Test Series - 7 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 - 7 | 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 - 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 )

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 black body at a temperature of 6000k emits a radiation whose intensity spectrum peaks at 600 nm. If the temperature is reduced to 5% k, the spectrum will peak at
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 19

By the kliien’s displacement law 

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

*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 31
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A BJT circuit has β = 50 & Vcc = 20V & uses a potential divider bias circuit with Rc = 2kΩ, R1=100kΩ & R2= 5kΩ. then Assuming Vbe = 0.2V which of the following statements is/are correct :-
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 31

In case of potential divider biasing,

Applying kirchoffs voltage law to base - Emitter circuit

Expressing Current in ‘mA ’ & resistances in ‘ kΩ ’ where as. 
0.952 = lb (4.76) + (0.2) + (51 x lb x 0.1)
Solving this above Eqn we get ;
[lb = 0.076mA] 

Vce = 20 - ( 3.8 x 2 ) - ( 3.876 x 0.1 )
(Vce = 12V)

GATE Physics Mock Test Series - 7 - Question 32
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The Mobility of e- in copper assuming that each atom contribute one free e- for conduction (Given : - Resistivity of copper is 1.7x1-6 ohm - cm , Atomic weight = 63.54 , density = 8.96 gm /c .c ) will be :-
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 32


*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 33
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For the given which of the following is/are correct
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 33

Let f(x) = x, 0 < x < 2π
and the Fourier series can be expressed as 






*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 34
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Consider the radioactive transformation a → B →C with decay constant λA and λB for elements A and B . C is a stable element . Assume that at t = 0, NA = N , NB = 0 and Nc = 0 where NA, NBand NC are the number of atoms of A, B and C respectively. Then which of the following is/are correct
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 34

Rate of disintegration of the element 
According to question A → B → C 
at t = 0, NA = N0 and NB = Nc = 0 
At any time t, for element A

for element B  
for element C, 
Again,  



*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 35
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Muons are elementary particles produced in the upper atmosphere. The have a life time of 2.2 us. Consider muons which are travelling vertically towards the earth’s surface at a speed of 0.998 C. For an observer on earth the height of the atmosphere above the surface of the earth is 10.4 km. Which of the follow­ing statements are true ?
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 35

Lifetime  


∴ Muon’s life time in earth’s frame 

Muon’s travelling at speed grater than 0.998C reach the earth’s surface . Muon’s reach the surface of earth because : the appearance thickness of atmosphere

Time taken to reach earth

t = 2.19 μ sec (just before the life time)

*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 36
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A uniform rod of mass m = 2kg and length L = 0.5 m is sliding along two mutually perpendicular smooth walls with the two ends P and Q having velocities Vp = 4m/sec and VQ = 3m/sec as shown, then
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 36



ω = 10 rad/se


*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 37
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A satellite of mass m is just placed over the surface of earth. In this position mechanical energy of satellite is E1 Now it starts orbiting round the earth in a circular path at height h = radius of earth. In this position, kinetic energy, potential energy and total mechanical energy of satellite are K2, U2 and E2 respectively. Then
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 37



*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 38
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Two charges + Q each are fixed at points C and D. Line AB is the bisector line of CD. A third charge +q is moved from A to B, then from B to C
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 38

Along the line AB, charge q is at unstable equilibrium position at B (when displaced from B along AB, net force on it is away from B, where as force at B is zero) Hence potential energy at B is maximum.
Along CD equilibrium of q is stable. Hence potential energy at B is minimum along CD.

*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 39
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A charged particle is moving along positive y-axis in uniform electric and magnetic fields.

Here E0 and B0 are positive constants, choose the correct options -
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 39


Depending on sign of q,  may be along positive z-axis or along negative z- axis.

Again, depending on the value q it may be along positive z-axis or along negative z-axis.
If q is positive,   comes along negative z-axis also.
But  comes along positive z-axis. so it may also path undeflected.

*Multiple options can be correct
GATE Physics Mock Test Series - 7 - Question 40
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One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure.
Its pressure at A is Po. choose the correct options from the following
Detailed Solution for GATE Physics Mock Test Series - 7 - Question 40


Information regarding P and T at C cannot be obtaining from the given graph. Unless it is mentioned that line BC passes through origin or not.

GATE Physics Mock Test Series - 7 - Question 41
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The muon has mass  and mean lifetime 2.2 ms in its rest frame. The mean distance traversed by a muon of energy   before decaying is approximately _____ km.

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 41

We know from einstein law 

given E = 315 MeV


We know mean distance travelled by muon is 

GATE Physics Mock Test Series - 7 - Question 42
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Consider two point charges q and λq located at points x = a and x = μa respectively. Assuming that sum of two charges is constant than what is value of λ for which the magnitude of electrostatic for is max __________ .

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 42




q(l + λ) = 0
λ = -1

GATE Physics Mock Test Series - 7 - Question 43
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Two particles of identical mass move in circular orbits under a central potential V (r) =  Let I1 and I2 be the angular momenta r1 r2 be radii of the orbits respec­tively. If  the value of  is

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 43

We know that, central force is conservative in central potential field

Here, (-) sign indicates the direction of force which is radially inward
In circular orbit, 
Ratio of angular momenta = 
Squaring both sides, we have 

GATE Physics Mock Test Series - 7 - Question 44
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A battery powers two circuits C1 and C2 as shown in the figure

The total current I drawn from the battery is estimated by measuring the currents I1 and l3 through the individual circuits. If I1 and l2 are both 200 mA and if the errors in their measurement are 3 mA and 4mA respectively, the error in the estimate of I is mA.

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 44

Let a and b be any two measured values and the error in this measurement are da and db then 
if y = a + b
then y + dy = (a + da) + (b + db)
⇒ y + Δy = a + b + Δa + Δb 
y + Δy = y + Δa + Δb 
Δi = 3 + 4 mA
ΔI = 7mA

GATE Physics Mock Test Series - 7 - Question 45
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A particle, of unit mass moves along the x-axis under the influence of a potential, V (x) = x (x - 2 )2 . The particle is found to be in stable equilibrium at the point x = 2. Find out the time period of oscillation of the particle.

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 45

The Potential is
V = x[x2 - 2x + x]
V = x3 - 2x2 + 4x
For equilibrium  

Given x0 = 2 then 

GATE Physics Mock Test Series - 7 - Question 46
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A 3 x 3 matrix has elements such that its trace is 11 and its determinant is 36. The eigenvalues of the matrix are all known to be positive integers. The largest eigenvalue of the matrix is _________ .

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 46

A 3 x 3 matrix have e eigen value. 
Let L1 l2l3 are three eigen values. 
So, I1 l2l3 = 36 
and Trac A = 11 
So, l2 + l2 + l3 =11

If I1 = 6, l2 = 3 and l3 = 2 
I1 + l2 + l3= 11
So , largest eigen value of matrix is(6)

GATE Physics Mock Test Series - 7 - Question 47
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A p - n junction is formed from germanium of conductivity 0.8 ohm-1 cm-1on p- side & 1.6 ohm-1 cm-1 on n-side. Calculate potential barrier at 300K (in V). (ni = 2.1 x 1013 cm-1) (Given μp = 2000 cm2/volt-sec and μn = 4000 cm2/volt-sec) (K = 1.38 x 10-16 erg per °K)

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 47


GATE Physics Mock Test Series - 7 - Question 48
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T h e current gain 'α’ of NPN transistor is 0.98. It is connected in the CB mode & gives a reverse saturation current Ico =12μA. Then the base current for an emitter current of 2mA will be _______(in μA ).

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 48

For NPN transistor, 
= 1.972 mA
again ; Ib - Ie - Ic = ( 2 - 1.972 ) mA = 28 μA

GATE Physics Mock Test Series - 7 - Question 49
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A gain transistor has a circuit gain of β = 60. If it is connected in a grounded base configuration, what theoretical a.c collector current (in mA) will flow when an a.c current of 2 mA flows through the emitter (Assume the collector potential to be const.)

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 49

GATE Physics Mock Test Series - 7 - Question 50
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The output voltage of a certain op-amp appears as shown in figure in response to a step input calculate its slow rate 

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 50

The slow rate (SR) 

GATE Physics Mock Test Series - 7 - Question 51
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In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another. 
ψ1 and ψ2 are two states defined by

where a is a constant.
The value of a for which y2 is orthogonal to y1 is ___________ .

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 51


for orthogonal condition -

1 + 2 + 3a = 0 
3a = - 3
a = -1

GATE Physics Mock Test Series - 7 - Question 52
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The magnetic field (in A m-1 ) inside a long solid cylindrical conductor of radius a 

What is the total current ( in A ) in the conductor ?

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 52

We know M.F(B) due to long solid cylindrical having radius a=0. 1m is

GATE Physics Mock Test Series - 7 - Question 53
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The vapour pressure p (in mm of Hg) of a solid, at temperature T, is expressed by in p = 23 - 3863/T and that of its liquid phase by In p = 19 - 3063/T. The triple point (in Kelvin) o f the material is __________ .

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 53

Vapour pressure p of solid is
logp = 23 - 3863/T ...(1)
Vapour pressure P of liquid phase is -
logp = 19 - 3063/T ...(2)
At triple point (logp)solid = (logp)liquid

GATE Physics Mock Test Series - 7 - Question 54
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A system has energy level E0, 2E0, 3E0...... . where the excited states are triply degenerate. Four non-interacting bosons are placed in this system. If the total energy of these bosons is 5E0, the number of microstates is ________ .

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 54

Four boson are placed in energy microstate so that total boson energy become 5E0, for this no. of microstates are

So, possible microstates are ‘5’.

GATE Physics Mock Test Series - 7 - Question 55
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A particle of mass 2 kg is moving such that at time t its position, in metre, is given by The angular momentum of the particle at t = 2 s about the origin, in kg m2 s-1, is _________ .

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 55

Angular momentum 


GATE Physics Mock Test Series - 7 - Question 56
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A car is moving with constant linear acceleration a along horizontal x-axis. A solid sphere of mass M and radius R is found rolling without slipping on the horizontal floor of the car in the same direction as seen from an inertial frame outside the car. The acceleration of the sphere in the inertial frame is ________ .

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 56

The torque about the point O is,
 where a’ is the acceleration of solid sphere during its motion, 
we know that, 


The net force  in the inertial frame is, 
Put the value of  in equation (1), we get

The acceleration of the sphere in the inertial frame is, 

GATE Physics Mock Test Series - 7 - Question 57
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In a Young’s experiment the upper slit is covered by a thin transparent plate of refractive index 1.1 and the lower slit is covered by another thin transparent plate of refractive index 1.9 but of thickness half the thickness of the first one. It is observed that the point O on the screen, where the central maxima fall before the insertion of the plates, now has 3/4th of the original intensity. It is also observed that what used to be the 4th maxima earlier lies below O whereas the 4th minimum is above O. Calculate the thickness (μm) of the upper plate. Take the wavelength of light to be 7200 A° and neglect any absorption of light.

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 57

The path difference

Intensity at O is  original intensity
 where is intensity each beam


Also, fringe shift  = 


For n = 4 ,  
Total thickness = 

GATE Physics Mock Test Series - 7 - Question 58
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A beam of plane-polarized light falls on a polarizer which rotates about the axis of the ray with angular velocity ω= 21 rad/s. Find the energy (mJ) of light passing through the polarizer per one revolution if the flux of energy of the incident ray is equal to φ = 4.0 m W.

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 58

When the polarizer rotates with angular velocity ω its instantaneous principal direction makes angle ωt from a reference direction which we choose to be along the direction of vibration of the plane polarized incident light. The transmitted flux at this instant is  ωt and the total energy passing through the polarizer per revolution is

GATE Physics Mock Test Series - 7 - Question 59
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The figure shows the results obtained during a photoelectric effect experiment where the stopping potential is plotted against the frequency of the incident radiation. The work function of the metal is close to _______ (in eV).

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 59

Kinetic energy of electron 
KE = hv - W
eVs = hv - W

At v = 0, Vs = - 2V

W = 2eV

GATE Physics Mock Test Series - 7 - Question 60
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Consider a maxwellian distribution of the energy of the molecules of an ideal gas in three dimension . let Eav and Erms denote the average energy and the root mean square energy, respectively. The magnitude of ratio  is _______

Detailed Solution for GATE Physics Mock Test Series - 7 - Question 60

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