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Q.

When a uniform solid sphere and a disc of the same mass and of the same radius rolls down a rough inclined plane from rest to the same distance, then the ratio of the time taken by them is :-

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a

15 : 14

b

$15^{2} : 14^{2}$

c

$\sqrt{14} : \sqrt{15}$

d

14 : 15

answer is C.

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Detailed Solution

The linear acceleration of the bodies rolling down an inclined plane,
$a \propto \frac{1}{1 + \frac{K^{2}}{R^{2}}}$
Hence for sphere, $a_{1} = 5 / 7$ and for disc
$a_{2} = 2 / 3$
From relation $s = \frac{1}{2} a t^{2} \Rightarrow t^{2} = \frac{2 s}{a}$
$\frac{t_{1}}{t_{2}} = \sqrt{\frac{a_{2}}{a_{1}}} = \sqrt{\frac{2 / 3}{5 / 7}} = \sqrt{14} : \sqrt{15}$

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