Rotational kinetic energy

Consider an electric dipole comprising two charges $+q$ and $-q$ each with mass $m$, separated by a fixed distance $d$ and initially at rest with its dipole moment pointing along $\hat\imath$. A uniform electric field $E\hat\jmath$ is turned on at time $t=0$ and it is turned off at $t=t_f$, when the dipole moment makes an angle $\theta_f$ with $\hat\imath$. Neglecting any sources of energy loss, correct option(s) is/are:

Amount of energy loss (in J) in the collision is:

A bar of mass $M = 1.00$ kg and length $L = 0.20$ m is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass $m = 0.10$ kg is moving on the same horizontal surface with $5.00\ \mathrm{m\,s^{-1}}$ speed on a path perpendicular to the bar. It hits the bar at a distance $L/2$ from the pivoted end and returns back on the same path with speed $v$. After this elastic collision, the bar rotates with an angular velocity $\omega$. Which of the following statement is correct?

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is -

A disc of mass 1 kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be $4\sqrt{\dfrac x{3R}}$ rad s$^{-1}$ where $x=$ ______.

($g=10$ ms$^{-2}$)

A thin and uniform rod of mass $M$ and length $L$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle 60° with vertical?

[$g$ is the acceleration due to gravity]

The total kinetic energy of the ring is

A diatomic molecule has moment of inertia $I$. By Bohr's quantization condition its rotational energy in the $n^{\text{th}}$ level ($n=0$ is not allowed) is

The ratio $x_1/x_2$ is

The loss of kinetic energy during the above process is