A solid sphere and a hollow cylinder roll up without slipping on...

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

\frac{n}{10}

. The value of

n

is______.

Correct answer

Step-by-step solution

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

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