$A$ symmetrical body of mass $M$ and radius $R$ is rolling without slipping on a horizontal surface with linear speed $v$. Then its angular speed is

An object of mass $10 \ kg$ and radius $0.5 \ m$ is rolling without slipping with a velocity of $2 \ m/s$. Its total kinetic energy is $32.8 \ J$. The radius of gyration of the object is .......... $m$.

Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If $R$ is the radius of the disc,the distance through which $P$ moves in one full rotation of the disc is:

$A$ uniform solid cylinder of mass $m$ and radius $R$ is set in rotation about its axis with an angular velocity $\omega_0$,then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction between the cylinder and plane is equal to $\mu$. The time after which the cylinder starts rolling without slipping is

Find the displacement of the point of contact with the ground when a ring of radius $R$ completes a half-rotation.

$A$ body is rolling without slipping on a horizontal plane. If the rotational kinetic energy of the body is $50 \%$ of its total kinetic energy, then the body is