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Q.

A uniform hollow sphere of radius $30 c m$ is released from rest on a rough inclined plane. The friction is sufficient to prevent any slipping. Find the angular velocity $(i n r a d / s)$ of the sphere, when its center of mass descends through a vertical height of $3 c m$ . $(g = 10 m / s^{2})$

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Detailed Solution

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Loss in PE=gain in KE

$m g h = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} \Rightarrow m g h = \frac{1}{2} m {(ω r)}^{2} + \frac{1}{2} (\frac{2}{3} m r^{2}) ω^{2} m \times 10 (\frac{3}{100}) = m \frac{5}{6} \times {(\frac{30}{100})}^{2} ω^{2} \Rightarrow ω = 2 r a d / s$

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A uniform hollow sphere of radius 30 cm is released from rest on a rough inclined plane. The friction is sufficient to prevent any slipping. Find the angular velocity (in rad/s) of the sphere, when its center of mass descends through a vertical height of 3 cm. g=10 m/s2