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

$A$ hollow sphere of mass $m$ and radius $R$ is rolling downward on a rough inclined plane of inclination $\theta$. If the coefficient of friction between the hollow sphere and incline is $\mu$,then ........

$A$ thin circular ring first slips down a smooth incline then rolls down a rough incline of identical geometry from the same height. The ratio of the time taken in the two motions is ........

$A$ solid sphere rolls purely on an inclined plane of inclination $\theta$. Which of the following statements are correct?
$(1)$ The friction force acting on the sphere is $f = \mu mg \cos \theta$.
$(2)$ Friction is a dissipative force.
$(3)$ Friction increases angular velocity and decreases linear velocity.
$(4)$ If $\theta$ decreases,friction decreases.

$A$ cylinder rolls up an inclined plane to a certain height and then rolls down. (It does not slip during the entire motion.) What is the direction of the frictional force acting on the cylinder?

$A$ sphere of mass $2 \, kg$ and radius $0.5 \, m$ is rolling with an initial speed of $1 \, m/s$ up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane,without slipping. How long will the sphere take to return to the starting point $A$? (in seconds)