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JEE Main 2019 (9 Apr, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2019 (9 Apr, Shift 1)

Q68JEE Main 2019 · 9 APR · SHIFT 1Medium

Rolling Motion

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane.: (i) a ring of radius R, (ii) a solid cylinder of radius R/2 and (iii) a solid sphere of radius R/4. If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:

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Answer: (a)

$h = \dfrac{v^2}{2g}(1+k)$ , independent of radius, so $h \propto (1+k)$ .
Ring $k=1$ : $2$ ; solid cylinder $k=\frac{1}{2}$ : $\frac{3}{2}$ ; solid sphere $k=\frac{2}{5}$ : $\frac{7}{5}$ .
Ratio $2 : \frac{3}{2} : \frac{7}{5} = 20 : 15 : 14$ (multiply by 10).
So the answer is (a) 20 : 15 : 14.

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