$A$ solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane of height $h$. When it reaches the foot of the plane,its rotational kinetic energy is ($g=$ acceleration due to gravity).

$A$ solid cylinder $(i)$ rolls down and $(ii)$ slides down an inclined plane. What is the ratio of the accelerations in these conditions?

$A$ solid cylinder of radius $R$ and mass $M$ rolls down an inclined plane without slipping and reaches the bottom with a speed $v$. The speed would be less than $v$ if we use:

Derive expressions for the kinetic energy and velocity of a body rolling without sliding down an inclined plane of inclination $\theta$.

Two uniform thin spherical shells are made from different materials. Both shells have a mass of $2 \,kg$ and an outer radius of $20 \,cm$. When they are both rolled down the same inclined plane without slipping,the times they take to cover equal distances differ by $1 \%$. If the thickness of the thinner shell is $0.5 \,cm$,the thickness of the other one is closest to ........... $\,cm$.

$A$ sphere of radius $R$ is rolling down an inclined plane whose angle of inclination is $\theta$. Its acceleration would be