A solid sphere,a disc,and a solid cylinder,al | vedclass

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(C) The time taken for an object to roll down an inclined plane is given by $t = \sqrt{\frac{2h}{g \sin^2 	heta} (1 + \frac{K^2}{R^2})}$.For a solid

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The solid sphere reaches the bottom first.

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(C) The time taken for an object to roll down an inclined plane is given by $t = \sqrt{\frac{2h}{g \sin^2 	heta} (1 + \frac{K^2}{R^2})}$.For a solid sphere,the moment of inertia $I = \frac{2}{5}MR^2$,so $\frac{K^2}{R^2} = \frac{2}{5} = 0.4$.For a disc and a solid cylinder,the moment of inertia $I = \frac{1}{2}MR^2$,so $\frac{K^2}{R^2} = \frac{1}{2} = 0.5$.Since the time $t$ is directly proportional to $\sqrt{1 + \frac{K^2}{R^2}}$,the object with the smallest value of $\frac{K^2}{R^2}$ will reach the bottom first.Comparing the values,$0.4 < 0.5$,therefore the solid sphere reaches the bottom first.

$A$ solid sphere,a disc,and a solid cylinder,all of the same mass and made of the same material,are allowed to roll down from rest on an inclined plane. Then,which of the following is true?

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