ઢોળાવવાળા સમતલ પરથી I જડત્વની ચાકમાત્રા ધરાવ | vedclass

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Question

Let Mass of sphere is $M$ and radius is $R$.

Moment of Inertia $I=\frac{2}{5} MR ^2$

$\Rightarrow v = R \omega$

$\Rightarrow 	ext { Total En

Vedclass · Accepted Answer

$28$

Vedclass · Answer

Let Mass of sphere is $M$ and radius is $R$.

Moment of Inertia $I=\frac{2}{5} MR ^2$

$\Rightarrow v = R \omega$

$\Rightarrow 	ext { Total Energy }=	ext { Rotational Energy }+	ext { Translational Energy }$

$\Rightarrow 	ext { Total Energy }=\frac{1}{2} I \omega^2+\frac{1}{2} Mv ^2$

$\Rightarrow 	ext { Total Energy }=\frac{1}{2} 	imes \frac{2}{5} MR ^2 	imes\left(\frac{ v }{ R }ight)^2+\frac{1}{2} M v^2=\frac{7}{10} Mv ^2$

$\Rightarrow \% 	ext { of Rotational Energy }=\frac{\frac{1}{5} Mv ^2}{\frac{7}{10} Mv ^2} 	imes$ $100=28.57 \approx 28 \%$

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