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  4. A solid cylinder, a solid sphere, a hollow sphere and a hollow cylinder, all of same mass and diameter are released from the same height at the same time on an inclined plane. If all the bodies roll down without slipping, then the body which will reach the bottom first, is

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Q. A solid cylinder, a solid sphere, a hollow sphere and a hollow cylinder, all of same mass and diameter are released from the same height at the same time on an inclined plane. If all the bodies roll down without slipping, then the body which will reach the bottom first, is

NTA AbhyasNTA Abhyas 2022

Solution:

If $l$ is the length of the inclined plane then the time taken by rolling the body to reach the bottom is
$t=\sqrt{2 l \frac{\left(M + \frac{I}{R^{2}}\right)}{M g sin \theta }}$ .
Moment of inertia $\left(I\right)$ is the least for the solid sphere among the other given bodies. Hence time taken will also be the least for the solid sphere.
Therefore, Solid sphere will reach the bottom first.