A spherical shell of 1kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is (a)/(3) R ^ 2 ω . The value of a

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Correct answer: C. 5

A spherical shell of 1kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure).

Angular momentum of a rotating and translating body is given by,

${L}_{O} = mvR + I\omega = mvR + \dfrac{2}{3}M{R}^{2}\omega$

For rolling, $v = \omegaR$

$⇒ {L}_{O} = m\omega{R}^{2}\left(1 + \dfrac{2}{3}\right) = \dfrac{5}{3}m\omega{R}^{2}$

Therefore, the value of $a = 5$ .

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