The following bodies,
1) a ring
2) a disc
3) a solid cylinder
4) a solid sphere,
of same mass ‘m’ and radius ‘R’ are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is
[Mark the body as per their respective numbering given in the question]

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answer is 4.

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Detailed Solution

The time takes by a rolling object to reach at bottom of inclined plane
$t = \sqrt{\frac{2 s}{a}} = \sqrt{\frac{2 s}{\frac{g \sin θ}{(1 + \frac{k^{2}}{R^{2}})}}} = \sqrt{\frac{2 s}{g \sin θ} (1 + \frac{k^{2}}{R^{2}})}$
$\Rightarrow t \propto \sqrt{1 + \frac{k^{2}}{R^{2}}}$
As $\frac{k^{2}}{R^{2}}$ is least for solid sphere among given object t is least for solid sphere
Solid sphere is given against to 4 in the question

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