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A spherical shell of 1 kg mass and radius R is rolling with angular velocity 𝜔 on horizontal plane (as shown in figures). The magnitude of angular momentum of the shell about the origin O is $\frac{a}{3} R^{2} ω$ . The value of $a$ will be:

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answer is C.

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Detailed Solution

$\begin{array}{l} {\vec{L}}_{0} = {\vec{L}}_{cm} + \vec{r} \times m \vec{V} \\ = \frac{2}{3} {mR}^{2} ω (- \hat{K}) + mVR (- \hat{K}) \\ = \frac{5}{3} {MR}^{2} ω (- \hat{K}) [V = Rω] \Rightarrow SO, a = 5 \end{array}$

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