A spherical shell of 1 ,kg mass and radius R is rolling with angular speed omega on horizontal plane

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6.System of Particles and Rotational Motion

hard

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 ..............

A

$2$

B

$3$

C

$5$

D

$4$

(JEE MAIN-2022)

Solution

$L _{0}=$ angular momentum of shell about $O$.

As shell is rolling

$\text { so } V _{ cm }=\omega R$

$L _{0}= mV _{ cm } R + I \omega$

$=1 \times \omega R \times R +\frac{2}{3} R ^{2} \omega$

$=\frac{5}{3} R ^{2} \omega$

$\text { so } a =5$

Standard 11

Physics

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