Rolling Motion — Prelims Questions

A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of angle $heta$. What is the acceleration of its center of mass?

A solid sphere and a hollow sphere of the same mass and radius are released from rest at the top of an inclined plane. Which one will reach the bottom first?

A disc of mass $M$ and radius $R$ rolls without slipping on a horizontal surface with a velocity $v_{CM}$ of its center of mass. What is the ratio of its translational kinetic energy to its rotational kinetic energy?

A wheel of radius $R$ rolls purely on a horizontal surface. What is the velocity of a point on its circumference at the top-most position?

A solid cylinder rolls without slipping on a horizontal surface. If its total kinetic energy is $K$, what is its translational kinetic energy?

A solid sphere rolls down an inclined plane without slipping. The minimum coefficient of static friction required for pure rolling is $\mu_{s,min}$. If the angle of inclination is $30^circ$, what is $\mu_{s,min}$?