An object is rolling on an inclined plane. Its linear and rotational kinetic energies are equal. The object is:

The moment of inertia of a solid cylinder about its axis is $I$. It is allowed to roll down an incline without slipping. If its angular velocity at the bottom is $\omega$,then the total kinetic energy $(K.E.)$ of the cylinder will be:

$A$ solid sphere rolls down an inclined plane and its velocity at the bottom is $v_1$. Then the same sphere slides down the plane (without friction) and let its velocity at the bottom be $v_2$. Which of the following relations is correct?

$A$ 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 $P$.

Three bodies,a ring,a solid cylinder,and a solid sphere,roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

$A$ solid cylinder and a disc of same radii are allowed to roll down a rough inclined plane from the top of a plane. The ratio of their times taken to reach the bottom of the inclined plane is