$A$ spherical shell and a solid cylinder of the same radius roll down an inclined plane. The ratio of their accelerations is ..........

$A$ hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\, m/s$ (as shown in figure). The maximum height with respect to the initial position covered by it will be $...........cm$.

$A$ ball rolls down an inclined plane,as shown in the figure. The ball is first released from rest from $P$ and then later from $Q$. Which of the following statement$(s)$ is/are correct?
$(i)$ The ball takes twice as much time to roll from $Q$ to $O$ as it does to roll from $P$ to $O$.
$(ii)$ The acceleration of the ball at $Q$ is twice as large as the acceleration at $P$.
$(iii)$ The ball has twice as much $K.E.$ at $O$ when rolling from $Q$ as it does when rolling from $P$.

$A$ 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.

Two solid spheres of different mass,radii,and density roll down a rough inclined plane under identical situations. Their time to come down is independent of their ............

When a sphere with moment of inertia $I$ rolls down an inclined plane,what percentage of its total energy is rotational kinetic energy?