The string of a step rolling wheel is pulled by applying force $F$ with different lines of action in two situations as shown. The wheel starts rolling without slipping due to application of the force.

 

Consider a ball of radius $R$, rolling without slipping on a horizontal plane. If the radius of gyration of the ball about an axis passing through its centre of mass is $K$, then what is the ratio of rotational kinetic energy to that of the total energy associated with the ball?

A particle of mass $m$ is moving horizontally at speed $v$ perpendicular to a uniform rod of length $d$ and mass $M=6m$. The rod is hinged at centre $O$ and can freely rotate in the horizontal plane about a fixed vertical axis passing through its centre $O$. The hinge is frictionless. The particle strikes and sticks to the end of the rod. The angular speed of the system just after the collision

Disc $A$ withradius $R$ is rolling on a rough floor. Disc $A$ strikes elastically with an identical smooth disc $B$. Assume no friction between $A, B$ and ground, $B$. Find the final velocities of $A$ and $B$ after long time? Given $V_0=5 \mathrm{m} {\mathrm{s}}^{-1}$ $R=1 \mathrm{m};$ mass of $disc\mathit{ }A, B=2 \mathrm{kg}$