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Rotational Motion

JEE Main level, numerical answer, medium

247 of 280

Question 247 of 280

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$ . The sphere and the cylinder reaches upto maximum heights $h_1$ and $h_2$ , respectively, above the initial level. The ratio $h_1: h_2$ is $\frac{n}{10}$ . The value of $n$ is______.

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Answer: 7

Gain in P.E. = Loss in K.E.

\mathrm{mgh}=\frac{1}{2} \mathrm{mv}^2\left(1+\frac{\mathrm{K}^2}{\mathrm{R}^2}\right)

\mathrm{h} \propto 1+\frac{\mathrm{K}^2}{\mathrm{R}^2}

\frac{\mathrm{h}_1}{\mathrm{~h}_2}=\frac{1+\frac{2}{5}}{1+1}=\frac{7}{5 \times 2}=\frac{7}{10}

\mathrm{n}=7

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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