GATE Physics Practice Quiz

Question 1

A particle of mass $m$ moves in one dimension under the potential $V(x)=\frac{1}{2}kx^2+\lambda x^4$, where $k>0$ and $\lambda>0$. For small oscillations about equilibrium, the angular frequency is

Accepted Answer

$\sqrt{\frac{k}{m}}$

Question 2

A particle is confined in a one-dimensional infinite square well $0<x<L$. If the system is in the state $\psi(x)=\sqrt{\frac{2}{L}}\sin\left(\frac{3\pi x}{L}\right)$, the expectation value of energy is

Accepted Answer

$\frac{9\pi^2\hbar^2}{2mL^2}$

Question 3

For a reversible adiabatic expansion of one mole of an ideal gas with heat capacity ratio $\gamma$, which relation is correct?

Accepted Answer

$PV^\gamma=\text{constant}$

Question 4

A point charge $q$ is placed at the center of a grounded conducting spherical shell of inner radius $a$ and outer radius $b$. The total charge induced on the inner surface and on the outer surface respectively are

Accepted Answer

$-q,0$

Question 5

A rigid body has principal moments of inertia $I_1<I_2<I_3$. According to Euler's equations for torque-free rotation, steady rotation about which principal axes is stable?

Accepted Answer

Axis corresponding to $I_1$

GATE Physics

Practice Quizzes

GATE Physics Practice Quiz

Simple Harmonic Oscillator Dynamics Fundamentals | GATE Physics