60 Questions MCQ Test - GATE Physics Mock Test Series - 6
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Let ψ0 and ψ2. denote respectively the ground state and second excited state energy eigenfunction of a particle moving in a harmonic oscillator potential with frequency ψ. If at time t the particle has the wavefunction,
The expectation value of the energy as a function of time
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 2
The expectation value of an operator that does not depend on the time and commutes with the Hamiltonian is constant in time. So, (E) will remain constant with time.
The first ball of mass m moving with the velocity v collides head on with the second ball of mass m at rest. If the coefficient of restitution is e, then the ratio of the velocities of the first and the second ball after the collision is
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 8
Here, m1= m2 = m, u1 = u, u2 = 0. Let v1, v2 be their velocities after collision.
According to principle of conservation of linear momentum,
mu + 0 = m (v1 + v2) or v1 + v2 = u ... (i)
By definition, ....(ii)
Add (i) and (ii),
Subtract (ii) from (i)
One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 9
When plane polarized light wave is incident on a quarter wave plate at θ= 45° angle then what is the nature of output wave.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 14
When plane polarised light is incident on quarter wave plate at θ = 45° then out light is circularly polarised. Because the phase difference provided by Q-W plate is and path difference is so, output light is circularly polarised
In a crystal whose primitives are 1.2A° 1.8A° and 2A°, along whose miller indices are (2, 3, 1) cuts intercept 1.2 A° along X - axis. What will be the length of intercepts along y and z - axes.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 22
Let p, q and r be the intercepts on X, Y, and Z axes respectively, then
where a, b and c are primitives and h, k and l Miller indices.
Given that a= 1.2 Å, b = 1.8 Å and c = 2.0Å and h = 2 , k = 3 and l = 1
= 0.6 : 0.6 : 2.0
As p = 1.2 Å
∴ 1.2 : q = 0.6 : 0.6
Similarly, 1.2 : r = 0.6 : 2.0
Thus the intercepts along Y and Z axes are 1.2 Å and 4 Å respectively.
Two equal negative charges -q are fixed at points (0, -a) and (0, a) on y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will be
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 23
Here Q is stay at point (2a, 0) which is very for in x-axis (2a).
Motion is simple harmonic only if Q is released from a point not very far from the origin on x-axis. (for small oscillations) other wise motion is periodic but not simple harmonic. So here such type of motion is not simple harmonic motion.
A uniform rod of length I is free to rotate in a vertical plane about a fixed horizontal axis through B. The rod begins rotating from rest from its unstable equilibrium position . When it has turned through an angle θ , its angular velocity ω is given as
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 24
When the rod rotates through an angle θ, the centre of gravity falls through a distance h. from ΔBG’ C,
The decrease in P.E. is equal to the kinetic energy of rotation
From equation (1) and (2), we get
A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 26
Now, at P (first minima) path difference between the rays reaching from two edges (A and B) will be
In a p-n junction diode not connected to any circuit
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 27
At junction a potential barrier/depletion layer is formed, with n-side at higher potential and p-side at lower potential. Therefore, there is an electric field at the junction directed from the n-side to p-side.
A planet of mass m and angular momentum L moves in a circular orbit in a potential v(r)= where k is a positive constant If the planet is slighthy perturbed, find angular frequency of radial oscillation.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 28
for stable point (orbit)
Therefore radius of stable circular orbit is Angular frequency of oscillation
about stable paint
What is the ratio of the nearest neighbour distance to the next nearest neighbour distance in a simple cubic crystal
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 29
We know, in a simple cubic lattice all atoms are at eight comers of cubic lattice of length a.
So, In a simple cubic lattice, the distance of nearest neighbour d1 = a
and the distance of next nearest neighbour d2 = a√2
An object of mass m moving with a velocity v is approaching a second object of the same mass but at rest. Which of the following are correct?
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 32
Let v1 is velocity of first mass after collision and v2 is velocity of second mass after collision.
By the conservation law of momentum
m1v = m1v1 + m2v2
m1 = m2 = m
⇒ mv = mv1 + mv2
v = v1 + v2
By conservation law of energy
Velocity of mass becomes zero whereas velocity of second mass attain the velocity of first. Now, the velocity of centre of mass is given
Hence the velocity of first w.r.t. centre of mass
That of second =
Total kinetic energy as seen from centre of mass =
A Germanium transistor with α = 0.98 gives a reverse saturation Current of 40μ A, when used in CB configuration when the transistor is connected in the CE mode with a base current of 0.2 ma. Then the following results have been obtained. Choose the correct options .
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 36
A particle of unit mass is thrown vertically upward with inifial speed v0. If is acted upon by a drag force bv2 in addition to gravity where b is constant and v is instantaneous velocity of particle. Then the speed of the particle when it returns to the point from where it was thrown,
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 37
In the presence of dray force, only the distance covered in upward and downware motion is common, for upward motion, initial speed = V0 final speed = 0, let height reaced = h
Equation of motion
on integrating we get, ________(1)
for downward motion, initial speed = 0 final speed = v (let), height descended = h
⇒ equation of motion
A solid cylinder is attached to a horizontal mass less spring on that it can roll without slipping along a horizontal surface. The spring constant k is 3 N/m. If the system is released from rest at a point in which the spring is stretched by 0.25 m .
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 38
An object travels along the x-direction with velocity in a frame O. An observer in a frame O’ sees the same object travelling with velocity The relative velocity of O ’ with respect to O. is ___________ (in the unit of C)
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 44
Water is filled in a cylindrical container to a height of 3m. The ratio of the cross sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s2)______ m2/sec2.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 45
Applying continuity equation at upper end and at hole
Further applying Bernoulli’s equation at two points
A source of sound of frequency 256 Hz is moving rapidly towards a wall with a velocity of 5m/s. How many beats per sec, will be heard if sound travels at a speed of 330 m/s, and observer is between the source and the wall?
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 46
In this situation, the source is moving towards the observer. Hence he will hear the sound of frequency n’ as given by
= 259.9 Hz
The same frequency is received by the wall. This frequency is reflected back towards observer. The wall with act as a source of frequency n’. Now source and observer both are at rest. The apparent frequency received by observer
n” = n’ = 259.9 Hz
∴ Beat frequency = n” - n’ = n’ ~ n’ = 0
The second order bright fringe in a single slit diffraction pattern is 1.4 mm from the center. The screen is 80 cm from the slit of width 0.80 mm. Assuming monochromatic incident light calculate the wavelength of light.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 47
As in case of diffraction at single slit second order maximum is approximately midway between 2nd and 3rd diffraction minima,
and as for small q, sin q = q = (y/D)....(2)
from equ.(1) and (2), we have
Two coherent plane waves of light of equal amplitude and each of wavelength 10π x 10-8 m, propagating at an angle of radian with respect to each other, fall almost normally on a screen. Find out the fringe-width (in mm) on the screen?
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 48
A quantity of air (y = 1.4) at 27°C is suddenly compressed to one third of its volume. Calculate the change in temperature in °C.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 49
When the air is compressed slowly, the heat generated conducts away to the surroundings. Thus it is an isothermal process, temperatures remains constant throughout, i.e., there is no change in temperature.
When the air is compressed suddenly, the process is adiabatic.
If T1, V1 be the initial and T2, V2 the final temperature and volume respectively, then
or T2 = 300 (3)04 = 465.5 K = (465.5 - 273) = 192.5°C
∴ Change in temperature T2 - T1 = 192°C - 27°C = 165°C.
Consider 1000 non - interacting , distinguishable particles in a two-level system at temp T. The energies of the levels are 0 and ε, whwere ∈> 0. In the high temperature limit (KBT > ε). What is the population of particles in the level with energy ε.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 51
let the total No. of non-interacting distinguishable particles are N
Population of particle in the level with energy ∈ is
So, the population of particles is the level with energy ∈ is 500.
In a silicon transistor, a change of 8.89 mA in the emitter current produces a change of 8.8 mA in the collector current. What change in the base current is necessary to produce an equivalent change in the collector current ?
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 52
What is the change in internal energy (in cal) when 0.004 kg. of air is heated from 0°C to 2°C. The specific heat of air at constant volume being 0.172 kilo cal/kg °C.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 55
From first law of thermodynamics
dQ = dU+ dW
where all quantities are measured in same units, say kilo cal.
Here air is heated at constant volume and hence no external work is done
i.e., dW = p. dV = 0.
Let m be the mass, cv the specific heat at constant volume and dT the rise in temperature of the air, the heat taken in by it is
dQ = m x cv x dT kilo cal.
Then from first law of thermodynamics
dU = dQ - dW = dQ
= m x cv x dT =0.004 x 0.172 x 2 = 1.376 x 10-3 kilo cal.
The Bragg angle corresponding to the first order reflection from (1,1,1) planes in a crystal is 30° when X - rays of wavelength 1.75Å are used. Calculate the interatomic spacing.
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 56
where a = interatomic distance
d = interplanar distance
h,k,l = Miller indices.
According to the problem h = k = I = 1 (being d111 plane)
q = 30°, I = 1.75 x 10-10m, n = 1
from bragg’s equation 2d sin q = nl, we have
A body of 100 gm. mass is moving with velocity m/sec. in an inertial frame which it self (frame) rotating with angular velocity radian/sec. with respect to a stationary reference frame. Then find out the magnitude of Coriolis force on moving body?
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 57
Water freezes at 0°C at atmospheric pressure (1.01 x 105 Pa). The density of water and ice at this temperature and pressure are 1000 kg/m3 and 934 kg/ m3 respectively. The latent heat of fusion is 3.34 x 105 J/kg. The pressure difference required for depressing the melting temperature of ice by 10°C is ______ (G Pa).
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 59
According to clausius clapeyron equation
dP = 1.73 x 108 Pa
dP = 0.173 x 109 Pa
dP = 0.173 GPa
If the Kα-radiation of Mo (Z = 42) has a wavelength of 0.71 Å , then evaluate the wavelength of the corresponding radiation of Cu (Z = 29).
Detailed Solution for GATE Physics Mock Test Series - 6 - Question 60
From Moseley’s law for Kα -line, we have
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