6.System of Particles and Rotational Motion
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ઘન ગોળા માટે ચાકગતિ અને રેખીયગતિ ઊર્જા નો ગુણોત્તર

A

 $\frac{2}{9}$

B

$\frac{2}{7}$

C

$\frac{2}{5}$

D

$\frac{7}{2}$

Solution

Rotational $K E=\frac{1}{2} I \omega^{2}$

but $\omega=\frac{v}{R}$

$\therefore$ Rotational $K E=\frac{1}{2} I \frac{v^{2}}{R^{2}}$

but the moment of inertia of a sphere is $I=\frac{2}{5} m R^{2}$

$\therefore$ Rotational $K E=\frac{1}{2}\left(\frac{2}{5} m R^{2}\right) \frac{v^{2}}{R^{2}}$

$\mathrm{Or}$

Rotational $K E_{R}=\frac{1}{5} m v^{2}$

Translational $K E_{T}=\frac{1}{2} m v^{2}$

Ratio $\frac{K E_{R}}{K E_{T}}=\frac{\frac{1}{5} m v^{2}}{\frac{1}{2} m v^{2}}=\frac{2}{5}$

Standard 11
Physics

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