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GATE Physics Mock Test Series - 8 - Physics


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60 Questions MCQ Test GATE Physics Mock Test Series - GATE Physics Mock Test Series - 8

GATE Physics Mock Test Series - 8 for Physics 2023 is part of GATE Physics Mock Test Series preparation. The GATE Physics Mock Test Series - 8 questions and answers have been prepared according to the Physics exam syllabus.The GATE Physics Mock Test Series - 8 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 - 8 below.
Solutions of GATE Physics Mock Test Series - 8 questions in English are available as part of our GATE Physics Mock Test Series for Physics & GATE Physics Mock Test Series - 8 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 - 8 | 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 - 8 - Question 1
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The entropy of a system, S, is related to the accessible phase space volume G by S = kBlnG(E, N, V) where E, N and V are the energy, number of particles and volume respectively. From this one can conclude that G

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 1

Two macroscopic system, which are in thermal contact, the required condition for the equilibrium is that their b parameter must be equal.
accessible phase space volume 
So   

on comparing
S = klnr(E,V,N)
and it is obvious that at equilibrium the accessible phase volume is maximum.

GATE Physics Mock Test Series - 8 - Question 2
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Let dw be the work done in a quasistatic reversible thermodynamic process. Which of the following statements about dw is correct?

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 2

The first law of thermodynamics can be given 
dQ = dU + dW
here dQ and dW both are path function and dU is state function. For making dW a perfect differential, we take dQ = 0 
So dU + dW = 0 
dW = -dU
and dQ = 0 occur in adiabatic process, so, dW0 is a perfect differential if the process is adiabatic.

GATE Physics Mock Test Series - 8 - Question 3
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A vector perpendicular to any vector that lies on the plane defined by x + y + z = 5, is

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

For finding the vector which is perpendicular to any vector on the plane is given by taking the gradient of that plane eqn.
The plane is φ = x - y + z - 5
New grad  

GATE Physics Mock Test Series - 8 - Question 4
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The eigenvalues of the matrix A  are
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 4

GATE Physics Mock Test Series - 8 - Question 5
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Two events, separated by a (spatial) distance 9 x 109 m, are simultaneous in one inertial frame. The time interval between these two events in a frame moving with a constant speed 0.8 c (where the speed of light c = 3 x 108 m/s) is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 5


Time measured at A, 
Time measured at B, 

GATE Physics Mock Test Series - 8 - Question 6
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Consider three polarizers P1 ,P2 and P3 placed along an axis as shown in the figure

The pass axis of P1 and P3 are at right angles to each other while the pass axis of P2 makes an angle θ with that of P1 . A beam of unpolarized light of intensity l0 is incident on P1 as shown . The intensity of light emerging from P3 is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 6

According to malus law the transmitted light intensity is proportional to the square of cosine of angle between polarizer and analyzer.

when light say passing through P1 the angle is q = 0° so
    .....(A)
when this polarized light passing through P2 which makes an angle q with P1 and P2 so
    ....(B)
Now P1 and P3 are 1 to each other so according to malus law the transmitted intensity

GATE Physics Mock Test Series - 8 - Question 7
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The commutator [x2, p2] is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 7

[ x2,p2] = [ x2,pp] = p [ x2,p ] + [ x2,p ]p
Since [A, BC] = B [A, C] + [A, B] C 

GATE Physics Mock Test Series - 8 - Question 8
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A point particle of mass m carrying an electric charge q is attached to a spring of stiffness constant k. A constant electric field E along the direction of the spring is switched on for a time interval T(whereT  Neglecting radiation loss, the amplitude of oscillation after the field is switched off is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 8

Let, in presence of electric field, the spring elongates by; distance ‘y’

The direction of motion is along y direction, then equation of motion is,



Now,

Now, apply boundary conditions, at t = 0, y = 0

where,  
Now, the amplitude of oscillation is, 

GATE Physics Mock Test Series - 8 - Question 9
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A transistor with β = 100 is used in CE configuration. The collector circuit resistance is 1kΩ& V∞= 20v. Assuming Vbe = 0 find the value of collector to base resistance such that quiescent collector to emitter voltage is 4v
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 9

GATE Physics Mock Test Series - 8 - Question 10
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The phenomenon known as ‘Early effect’ in a bipolar transistor refers to a reduction of the effective-basewidth caused by___
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 10

In a bipolar transistor, the increase in the depletion region of the reverse biased junction, tends to decrease the width of the base with increased reverse voltage. This in turn causes the current gain to increase with increased voltage resulting in a nearly linear increase in current even with the device in the saturation.

GATE Physics Mock Test Series - 8 - Question 11
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A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant, r is the distance of the bead from the origin. The momentum conjugate to r is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 11

The momentum conjugate to r is = 

GATE Physics Mock Test Series - 8 - Question 12
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A particle of mass m is in a potential given by

where a and r0 are positive constants. When disturbed slightly from its stable equilibrium position, it undergoes a simple harmonic oscillation. The time period of oscillation is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 12


where a & r0 is positive constant 

For stable equilibrium 

We know that the time period of oscillation is

where K is force constant

GATE Physics Mock Test Series - 8 - Question 13
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A planet of mass m moves in a circular orbit of radius r0 in the gravitational potential V(r) =  where k is a positive constant. The orbital angular momentum of the planet is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 13

Gravitational potential 
Gravitational Force (F)  

momentum (p) = mv = 
Anglax momentum(L)  = 

GATE Physics Mock Test Series - 8 - Question 14
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The solution of the differential equation

subject to the boundary conditions y(0) = 1 and y(∞) = 0, is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 14

The differential equation

according to boundary conditions; y(0) = 1

equation 3 will be satisfy if or only if 

 {adding and subtracting e1/2}

GATE Physics Mock Test Series - 8 - Question 15
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In an interference pattern formed by two coherent sources, the maximum and the minimum of the intensities are 9I0 and I0, respectively. The intensities of the individual waves are
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 15

The max & min intensities by two coherent sources is given by:-

Solving the above two eq, we get 
l1 = 4l0       &       l2 = l0

GATE Physics Mock Test Series - 8 - Question 16
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Identify the CORRECT statement for the following vectors 
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 16

The determinate is not equal to zero

have no mutual relation so it is linearly independent

GATE Physics Mock Test Series - 8 - Question 17
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Identify, the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, ED and EF are conduction band, valence band, impurity level and Fermi level, respectively.
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 17

As doping with Arsenic Will change the pure silicon Semiconductor into n - type & in n - type SC the free charge carriers are present does to CB because Arsenic is a pentavalent atom thus the atom Thus the fermi Energy level will lie slightly above the middle of the Energy gap & does to ED.

GATE Physics Mock Test Series - 8 - Question 18
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A pendulum suspended from the ceiling of the train is at rest. What will be the time period of pendulum if the train accelerates at 10 m/s2 (Take g = 10 m/s2)
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 18


For simple pendulum T = 
T = 2 se.                   ......(B)
So, from eq.(A) and (B),

GATE Physics Mock Test Series - 8 - Question 19
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A rod of proper length l0 oriented parallel to the x-axis moves with speed 2c/3 along the x-axis in the. S-frame, where c is the speed of the light in free space. The observer is also moving along the x-axis with speed c/2 with respect to the S-frame. The length of the rod as measured by the observer is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 19

For finding the length of rod firstly finding the relativistic velocity which is equal to


Now the measured length

GATE Physics Mock Test Series - 8 - Question 20
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Given  is a constant vector and r is the position vector. The value of   where C is a circle of unit radius centered at origin is _____ .
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 20




GATE Physics Mock Test Series - 8 - Question 21
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A system has two energy levels with energies ε and 2ε. The lower is 4-fold degenerate while the upper level is doubly degenerate. If there are N noninteracting classical particles in the system, which is in thermodynamic equilibrium at a temperature T, the fraction of particles in the upper level is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 21


So, partition function Z = 

so, fraction of particles in the upper level is

GATE Physics Mock Test Series - 8 - Question 22
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A spherical conductor of radius a is placed in a uniform electric field  the potential at a point  for r > a, is given by

where r is the distance of P from the centre O of the sphere and q is the angle OP makes with the z-axis.

The charge density on the sphere at q = 30° is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 22

Potential f (r, θ ) 
We know electric field due to conducting sphere is


E F. at the surface sphere of sphere and at θ = 30°


So, surface charge density s 

GATE Physics Mock Test Series - 8 - Question 23
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The solution of the differential equation for  subject to the initial conditions  is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 23




So, solution of differential equation
y(t) =t sin h (t)

GATE Physics Mock Test Series - 8 - Question 24
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A particle of mass m is confined in the potential

Let the wave function of the particle be given by

where y0 and y1 are the eigen functions of the ground state and the first excited state respectively. The expectation value of the energy is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 24


y0 ground state eigen function y,® first excited state eigen function energy eigen value E =(n+1/2)ℏω

for ground state n = 0, E = 
for first excited state n =1, E = 

 

GATE Physics Mock Test Series - 8 - Question 25
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Two magnetic dipoles of magnitude m each placed in a plane as shown. The energy of interaction is given by
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 25

Angle between dipoles = 90°
Angles made by diploes with position vector (d) = 45 ° 
Magnetic interaction energy 
U = M.B

GATE Physics Mock Test Series - 8 - Question 26
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A mass m is constrained to move on a horizontal frictionless surface. It is set in circular m otion with radius r0 and angular speed w0 by an applied force com municated through an inextensible thread that passes through a hole on the surface as shown in the figure. This force is then suddenly doubled. The magnitude of the radial velocity of the mass
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 26

The particle is moving in a circular motion with radius r0 and angular speed ω0 by an applied force F applied through an inextensible thread passing through hole.
The circular motion of the particle is, 
Now. when we doubled the force.

Subtract equation (A) from (B). we get



As the force increases, r will decrease and hence, velocity of particle will decrease till the fall into the hole.

GATE Physics Mock Test Series - 8 - Question 27
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For the BJT circuit shown, assume that the β of the transistor is very large and VBE = 0.7V. The mode of operation of the BJT is ___
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 27

For saturation, VBE > 0.7 volts In saturation condition,

Apply KVL in base circuit 

So, operate in saturation region.

GATE Physics Mock Test Series - 8 - Question 28
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If for a silicon n-p-n transistor, the base-to-emitter voltage (VBE) is 0.7V and the collector-to-base voltage (VCB) is 0.2V. then the transistor is operating in the___
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 28

VB = 0.7V [Forward-biased]
and VBC = -VCB = - 0.2V (Reverse-biased)
Hence, the transistor operates normal active mode.

GATE Physics Mock Test Series - 8 - Question 29
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Assuming VCEsat = 0.2V and β= 50. the minimum base current (lB) required to drive the transistor in the given figure to saturation is___
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 29

The minimum value of base current to derive the transistor into saturation is

From the figure given ,

GATE Physics Mock Test Series - 8 - Question 30
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In the voltage regulator shown in the given figure, the load current can vary from 100 mAto 500 mA. Assuming that the Zener diode is ideal (i.e, the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of R is    
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 30

From the circuit given, we have


( Zener knee current is negligibly small) 
or- 14Ω < R < 70Ω
Hence, required value of R = 14Ω [closed min value]

GATE Physics Mock Test Series - 8 - Question 31
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A converging lens is used to form an image on screen. When the upper half of the lens is covered by an opaque screen.
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 31

When upper half of the lens is covered image is formed by the rays coming from lower half of the lens. OR image will be formed by the less number of rays. Therefore, intensity of image will decrease. But complete image will be formed.

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 32
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A beam of light of wavelength 400 nm and power 1.55 mQ is directed at the cathode of a photoelectric cell, (given he = 1240 ev). If only 10% of the current due to these electrons is i . If the wavelength o f light is now reduced to 200 nm, keeping its power the same, the kinetic energy of the electrons is found to increase by a factor of 5. The stopping potentials for the two wavelength are S1 and S2. Then
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 32

Wavelength of incident light λ= 400nm
P = 1.55 mW
Energy of one photon 
Number of photons falling per second

Number of electrons ejected is 10% of number of photon falling per second .
N = 0.1 n

Current constipated by flow of ejected electrons

Kinetic theory of ejected electron = Photon - Work function Energy of incident

Where λ = 400nm is reduced to λ = 200nm , the KE increases by 5 times.

Subtracting equation (A) from (B)

Stopping potential

Stopping potential

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 33
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In a compton experiment the ultraviolet light of wavelength 2000 A° is scattered from an electron at rest. What should be the minimum resolving power of an optical instrument to measure the compton shift. If the observation is made at 60° and 90° with respect to the direction of the incident light ?
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 33

For uv light of wavelength 2000 A°, 
Scallered at an angle θ


Minimum resolving power of instrument required to measure the compton effect 

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 34
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X-Rays of wavelength λ = 0.612 A ° are scattered by free electron (compton collision). Then which of the following statements is/are correct
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 34

Wavelength of scattered radiation

Kinetic energy imparted to the electron 

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 35
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A particle of mass m and energy E moving in the positive x- direction, encounters a one - dimensional potential barrier at x = 0. The barrier is defined by 

If the wave function of the particle in the region x < 0 is given as Aelkx + Be-ikx. If  = 0.4, then
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 35

Assuming region (I) for x < 0 and region (II) for x > 0 for region (I), wave function

For region (II), we can write wave function as

At the boundary , x = 0


According to the question



Reflection coefficient

Transmission coefficient 
T = 1 - R = 0.84

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 36
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A resistor of 1KΩ and an inductor of 5mH are connected in series with a battery of emf 4v through a switch. The switch is closed at time t = 0. (use e3 = 20)
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 36


When the switch is closed at t = 0. The circuit acts as charging R - L circuit. Instantaneous current flowing through the circuit can be given as

i0 → steady state current

Putting t = 15 x 10-6 sec, L = 5 x 10-3 H and R = R = 1KΩ

Again, heat dissipated through the resistor during first t second is

Putting t = 15 μsec, we will get 
H = 12.799 x 10-10 J

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 37
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One mole of an ideal gas (r = 1.5) is at pressure of 100 K Pa and a temperature of 300 K. Initial the state of the gas is at the point a of the PV diagram shown. The gas is taken through a reversible cycle a→ b→ c→ a The pressure at point b is 200 K Pa. Then
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 37

For path 

Comparing with the process PV-X = constant 

During process be, ΔWbc = 0
work done ΔWca = Pdv = 100x103(1m3) = 100KJ
again process ab

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 38
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In two figures
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 38


Here hT = distance of hole from top surface of liquid and hB = distance of hole from bottom surface.

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 39
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A coil of area 2m2 and resistance 4Ω is placed perpendicular to a uniform magnetic field of 4T. The loop is rotated by 90° in 0.1 sec. Choose the correct options-
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 39


This current is not constant. So, we cannot find the heat generated unless current function with time is not known .

*Multiple options can be correct
GATE Physics Mock Test Series - 8 - Question 40
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A Voltage 200 cos 100 t is applied to a half wave rectifier with load resistance of 5kΩ . Rectifier may be represented by an ideal diode in series with a resistance of 1kΩ
Then which of the following statements is/are correct :-
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 40


GATE Physics Mock Test Series - 8 - Question 41
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An unpolarized lightwave is incident from air on a glass surface at the Brewster angle. Calculate the angle (in degree) between the reflected and the refracted wave.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 41


Brewster angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface with no reflection. When unpolarized light is incident at this angle the light that is reflected from the surface is therefore perfectly polarized.
Then the Brewster angle qs

and the angle between Reflected Ray and Refracted Ray will be 90°.

GATE Physics Mock Test Series - 8 - Question 42
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y1 and y2 are two orthogonal states of a spin 1/2 system. It is given that

where represent the spin-up and spin-down states, respectively. When the system is in the state y2, its probability to be in the spin-up state is __________ .

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 42


When the system is in state y2. its probability to be in the spin up state is

GATE Physics Mock Test Series - 8 - Question 43
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A one dimensional harmonic oscillator is in the superposition of number states, |nn, given by

The average energy of the oscillator in the given state is __________ hw.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 43

A one dimensional harmonic oscillator is in the superposition of number states |nn, given by

The energy of the |nn state in one dimensional harmonic oscillator

Total energy 

GATE Physics Mock Test Series - 8 - Question 44
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A ball of mass m. initially at rest, is dropped from a height of 5 meters. If the coefficient or restitution is 0.9, the speed of the ball just before it hits the floor the second time is approximately________ m/s (take g = 9.8 m/s2)

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 44

As we know that
The coefficient of restitution  = 
The velocity at the time of hitting with floor is = 
Velocity of approaching = 

GATE Physics Mock Test Series - 8 - Question 45
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When an ideal monoatomic gas is expanded adiabatically from an initial volume V0 to 3V0. its temperature changes from T0 to T . Then the ratio  is

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 45

By the equation of adiabatic process 

GATE Physics Mock Test Series - 8 - Question 46
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Let Es denote the contribution of the surface energy per nucleon in the liquid drop model. The ratio  is ________ .

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 46

We know that semi empirical mass formula is

Surface Energy Es = a5A2/3
Surface Energy per nucleon is = 

GATE Physics Mock Test Series - 8 - Question 47
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A particle moves in a plane with velocity such that  The time dependence of the magnitude of the velocity  = 5t. It is given that r = 1 ,θ =0 and v r > 0 at t = 0. (In the following, you may use e3 ≈ 20.) At what time (in sec.) will θ become 4 radian?

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 47


where c is arbitrary constant which can be evaluated by using initial condition 
r = 1 at 9 = θ ⇒ c = 1
 Equation of trajectory r(θ)
Magnitude of velocity  = 5t

Integrating

where c is arbitrary constant which can be evaluated using initial condition

GATE Physics Mock Test Series - 8 - Question 48
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A body of mass 1 kg moves under the influence of a central force, with a potential energy function V(r) =  Joule, where r is in meters. It is w l found to move in a circular orbit of radius r = 2 m. (In the following, you may use e3 ≈ 20). Find its total energy E. (in mJ)

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 48

Central Force potential energy

Effective potential = 

The body moves in a circular orbit of radius r = 2m
So, energy of the system will always be equal to effective potential Ve at r =2m
Also, Ve will be minimum at r = 2m and  will be zero at r = 2m 

For circular motion

GATE Physics Mock Test Series - 8 - Question 49
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A cylinder of 1 kg mass and 0.02 m diameter left at the top of an inclined plane of height 1 m rolls down without slipping. (Take g = 9.8 ms-2). Find the velocity of center of mass of cylinder on reaching the bottom of inclined plane (in m/sec).

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 49


The kinetic energy of cylinder when it reaches the bottom = potential energy of the cylinder at the top = mgh = 1 x 9.8 x 1 = 9.8 J 
Kinetic energy kE = kE of translation + kE of rotation

Kinetic energy at bottom = 9.8 J

GATE Physics Mock Test Series - 8 - Question 50
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X-Rays of wavelength λ = 0.612 x 10-10 m are scattered by free electrons (Compton collision). Calculate the corresponding kinetic energy in eV imparted to the electron.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 50

Wavelength of X-ray, λ = 0.612 x 10-10 m = 0.612 A0 
Compton shift in wavelength

h = planck’s constant 
m0 = rest mass of electron
c = speed of light
φ = Angle b which radiation gets scattered 

Kinetic energy imparted to the electron 
KE = Change in energy possessed by photon

GATE Physics Mock Test Series - 8 - Question 51
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A parallel beam of light of diameter 1.8 cm contains two wavelengths 4999.75 Å and 5000.25 Å. The light is incident perpendicularly on a large diffraction grating with 5000 lines per centimeter. Using Rayleigh criterion, find the least order at which the two wavelengths are resolved.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 51

Resolving power required to resolve two wavelengths = 
So, Resolving power of grating must be greater than 10000 
Resolving power of grating
R = Nn ≥ 10000

So, least order at which two wavelengths are resolved nmin = 2

GATE Physics Mock Test Series - 8 - Question 52
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If differential gain of an opamp is Avd = 3500 % & Common mode gain (AcM) = 0.35. Then CMRR will be ______ dB.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 52

CMRR - 20 log 
CMRR = 80dB

GATE Physics Mock Test Series - 8 - Question 53
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The output in the above circuit will be ______ V.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 53


[Vo = +3V]

GATE Physics Mock Test Series - 8 - Question 54
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An aircraft, which weights 12000 kg when unloaded , is on a relief mission , carrying 4000 food packets weighing 1 kg each. The plane is gliding horizontally with its engines off at a uniform speed of 540 kmph when the first food packet is dropped. Assume that the horizontal air drag can be neglected and the aircraft keeps moving horizontally. If one food packet is dropped every second , then the distance between the last two packet drops will be _______ m.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 54

The mass of an aircraft = 12000 kg
Uniform speed of aircraft is 
The distance between the last two packet drops will be equal to the covered distance in one second = 150 m.

GATE Physics Mock Test Series - 8 - Question 55
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In the temperature range 100-1000 C, the molar specific heat of a metal varies with temperature T (measured in degrees Celsius) according to the formula Cp =(1 + T /5 ) J-deg C-1-mol-1. If 0.2 Kg of the metal at 300 C, the final equilibrrium temperature, in degree C, will be ________ .
[Assume that no heat is lost to radiation and /or other effects .]

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 55


m1 = 0.2. T1= 600 C 
m2 = 0.1, T2 = 300 C
We know at the thermal equilibrium 
Heat absorb = Heat gain


3T2 + 30T = 15000 + [3002 + 2(600)2]  
T = 519

GATE Physics Mock Test Series - 8 - Question 56
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On a planet having the same mass and diameter as the Earth, it is observed that objects weightless at the equator. Find the time period of rotation of this planet in minutes (as defined on the Earth).

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 56

We know that g '= g - ω2Rcos2λ
At equator     
If ω' = 17ω then the object become weightloss at the equator.
Then the time period of rotation of this planet in minutes is

GATE Physics Mock Test Series - 8 - Question 57
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The Zener diode in the regulator circuit shown in the figure has a Zener voltage of 5.8 Volts and a Zener knee current of 0.5 mA. The maximum load current drawn from this circuit ensuring proper functioning over the input voltage range between 20 and 30 volts, is _____ mA.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 57

Since. VE = 5.8 V always remains constant, therefore maximum load current
when volts (V) is maximum i.e. = 30V
 ∴  30 = 1000 x lmax + 5.8
∴ lax = 24.2 mA

GATE Physics Mock Test Series - 8 - Question 58
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The centre tap full wave single-phase rectifier circuit uses 2 diodes as shown in the given figure. The rms voltage across each diode is _______ V.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 58

PIV across each diode = 2 x 280 √2 Volts.
when the diode is conducting (during half cycle ) the voltage across the diode is zero.
Hence, rms value of the voltage of the voltage across the diode

GATE Physics Mock Test Series - 8 - Question 59
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If  for a transistor, than the value of Lc will be ____  mA.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 59

GATE Physics Mock Test Series - 8 - Question 60
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The output voltage for the summing amplifier shown in figure is ______ V.

Detailed Solution for GATE Physics Mock Test Series - 8 - Question 60

Rf= 10 kΩ
and R = R1 = R2 = 1.0 kΩ

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Important Questions for GATE Physics Mock Test Series - 8

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GATE Physics Mock Test Series - 8 MCQs with Answers

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Online Tests for GATE Physics Mock Test Series - 8 GATE Physics Mock Test Series

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