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  4. A spherical shell of 1 kg 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) R2 ω. The value of a will be :

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Q. A spherical shell of $1 \,kg$ mass and radius $R$ is rolling with angular speed $\omega$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin $O$ is $\frac{a}{3} R^{2} \omega$. The value of a will be :Physics Question Image

JEE MainJEE Main 2022System of Particles and Rotational Motion

Solution:

$L _{0}=$ angular momentum of shell about $O$.
As shell is rolling
so $ V _{ cm }=\omega R $
$ L _{0}= mV _{ cm } R + I \omega $
$=1 \times \omega R \times R +\frac{2}{3} R ^{2} \omega$
$=\frac{5}{3} R ^{2} \omega $
so $ a =5$