GATE Physics Mock Test Series - 4 - Physics MCQ

The expectation value of energy when the state of the harmonic oscillator is described by the following wave function 

where ψ₀(x,t) and ψ₂(x,t) are wave functions for the ground state and second excited state respectively :-

While using second latent heat equation  , the specific heat of steam is negative in the following condition :-

For silver, the specific heat at constant pressure in the range of 50 K to 100 K is given by C_p = 0.076 T - 0.00026 T² - 0.15 cal mol^-1 deg^-1 where T is the kelvin temperature. If 2 mole of silver are heated from 50 K to 100 K. Calculate the change in entropy

A particle describes a circular orbit under the influence of an attractive central force directed toward a point at the center. The force inversely proportional to

An astronaut moves in a super spaceship travelling at a speed of 0.64C. The astronaut observes a photon approaching him from space. The speed of photon with respect to the astronaut i s ________ .

Half life of a radioactive materials is 4 days. After 20 days, the fraction remaining undecayed will be -

After being hit, a golf ball reaches a maximum height 60 m with a speed of 30 m / sec. Right after being hit, the speed of the ball is (take g = 10 m/sec²)

The vector field  in cylindrical polar coordinates is

One mole of monoatomic ideal gas is initially at pressure P₀ and volume V₀. The gas then undergoes a three - stage cycle consisting of the following processes:
(A) An isothermal expansion till it reaches volume 2 V₀ and heat Q flows into the gas.
(B) An isobaric compression back to the original volume V₀
(C) An isochoric increase in pressure till the original pressure P₀ is regained. The efficiency of this cycle can be expressed as

The normalized wave function of a particle can be written as

Where (x) are the normalized energy eigenfunction of a given Hamiltonian. The value of N is

The commutator of two matrices A and B are defined as 
[A, B] = AB - BA 
{A, B} = AB + BA
If [A,B] = 0. We can write [A,B,C] =

A Solid cylinder of height H, radius R and density P, floats vertically on the surface of a liquid of density_pThe cylinder will be set into oscillatory motion when a small instantaneous downward force is applied. The frequency of oscillation is

Consider a hollow charged shell of inner radius a and outer radius b. The volume charge density is  (K is constant) in the region a < r < b. The magnitude of the electric field produced at distance r > a is

The wave function of a state of the hydrogen atom is given by  where , denotes the normalized eigenfunction in the usual notation. The expectation value of L_z in the state 

A planet of mass m moves in the gravitational field of the sun (mass M). If the semi-major and semi-minor axis of the orbit are a and b respectively. The angular momentum of the planet is

Consider an infinite conducting sheet in the xy-plan with a time dependent current density kt  where K is a constant. The vector potential at (x,y,z) is given by   The magnetic field  is

Water is flowing through a tube as shown. The cross section area at A & C are equal and greater than the cross-sectional area at B. If the flow is steady, then the pressure on the walls at B is

A gas of N non-interacting particles is in thermal equilibrium at temperature T. Each particle can be in any of the possible non-degenerate states of energy . The average energy per particle of the gas, when  <<< 1, is

A plane electromagnetic wave is propagating in a lossless dielectric. The electric field is given by

where c is the speed of light in vacuum, E₀, A, and K_o, are constants and and are unit vectors along the x-axis and z-axis
The relative dielectric constant of the medium  and the constant A are

A plane polarized electromagnetic wave in free space at time t = 0 is given  The magnetic field  is given by

A circular loop of mass M and radius a rolls without slipping with constant angular speed ω along the horizontal x-axis in the x-y plane. When the centre of the hoop is at a distance d =   from the origin, the magnitude of the total angular momentum of the loop about the origin is

A particle is incident with a constant energy E on a one dimensional potential barrier as shown in the figure. The wave function in regions I and II are respectively

The frequency response curve of a damped forced oscillator will be of the form (R-amplitude and V_R- frequency ratio) :

A voltage applied to an X-Ray tube being increased η = 1.5 times, the shortwave limit of an X-Ray continuous spectrum shifts by Δλ = 26 pm. Find the initial voltage applied to the tube.

Metallic copper is know to form cubic crystals and the lattice constant is measured from X-ray diffraction studies to be about 0.36 nm. If the specific gravity of copper is 8.96 and its atomic weight is 63.5, one can conclude that

In a simple cubic structure of lattice constant a, one plane among a set of parallel planes intercepts x,y, and z- axis 2a, a and a respectively. The interplanar spacing is

Consider a doped semiconductor having the electron and the hole mobilities μ_n and μ_p respectively. Its intrinsic carrier density is n_i The hole concentration p for which the conductivity is minimum at a given temperature is