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 reach upto maximum heights h₁ and h₂ respectively, above the initial level. The ratio h₁: h₂ is n/10. The value of n is __________. Numerical answer type. Work it out, then open the answer.

Answer: 7. h = v²/2g(1+k), so h ∝ (1+k). Solid sphere k = 2/5: 1+k = 7/5; hollow cylinder k = 1: 1+k = 2. (h₁)/(h₂) = 7/5/2 = 7/10. So n = 7.

A solid sphere and a hollow cylinder roll up without slipping on same… | JEE Main 2024 (4 Apr, Shift 1)

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Rolling Motion

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 reach 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 __________.

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

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Answer: 7

$h = \dfrac{v^2}{2g}(1+k)$ , so $h \propto (1+k)$ .
Solid sphere $k = \frac{2}{5}$ : $1+k = \frac{7}{5}$ ; hollow cylinder $k = 1$ : $1+k = 2$ .
$\dfrac{h_1}{h_2} = \dfrac{7/5}{2} = \dfrac{7}{10}$ .
So $n = 7$ .

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