ચાકગતિમાં શુધ્ધ રોલિંગ (ગબડતી ગતિ) દરમિયાન ની | vedclass

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Question

(c)

$K _{	ext {Rother }}= K _{	ext {Trenstation }}+ K _{	ext {rotaton }}$

$=\frac{1}{2} m v^2+\frac{1}{2} l \omega^2$

$=\frac{1}{2} m R^2

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(c)

$K _{	ext {Rother }}= K _{	ext {Trenstation }}+ K _{	ext {rotaton }}$

$=\frac{1}{2} m v^2+\frac{1}{2} l \omega^2$

$=\frac{1}{2} m R^2 \omega^2+\frac{1}{2}\left|\omega^2=\frac{1}{2}ight| \omega^2\left(1+\frac{m R^2}{1}ight)$

$\Rightarrow$ ratio $=\frac{K_{	ext {waton }}}{K_{	ext {total }}}=\frac{\frac{1}{2} I ^2}{\frac{1}{2} I_{\omega^2}\left(1+\frac{m R^2}{1}ight)}$

$=\frac{1}{1+\frac{m R^2}{1}}$

For disc,

$	ext { Ratio }=\frac{1}{1+\frac{m R^2}{\left(\frac{m R^2}{2}ight)}}=\frac{1}{3}$

Solid sphere

$	ext { Ratio }=\frac{1}{1+\frac{m R^2}{\frac{2}{5} m R^2}}=\frac{2}{7}$

Ring

$	ext { Ratio }=\frac{1}{1+\frac{m R^2}{m R^2}}=\frac{1}{2}$

Hollow sphere ratio $=\frac{1}{1+\frac{m R^2}{\frac{2}{3} m R^2}}=\frac{2}{5}$

Hence $ring$ correct option.

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