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JEE Main 2021 (20 Jul, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2021 (20 Jul, Shift 1)

Q57JEE Main 2021 · 20 JUL · SHIFT 1Medium

Rolling Motion

A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time 't1'. When it rolls down the plane, it takes time t2. The value of $\frac{t_2}{t_1}$ is $\sqrt{\frac{3}{x}}$ . The value of x will be _______________.

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Slipping: $a_1 = g\sin\theta$ ; rolling disc: $a_2 = \frac{2}{3}g\sin\theta$ .
For the same $L$ from rest, $t \propto \dfrac{1}{\sqrt{a}}$ .
$\dfrac{t_2}{t_1} = \sqrt{\dfrac{a_1}{a_2}} = \sqrt{\dfrac{3}{2}}$ , so $x = 2$ .

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