A hollow sphere of radius R and mass m is fully filled with water of mass m . It is rolled down a ho

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6.System of Particles and Rotational Motion

hard

$A$ hollow sphere of radius $R$ and mass $m$ is fully filled with water of mass $m$. It is rolled down a horizontal plane such that its centre of mass moves with a velocity $v$. If it purely rolls

A

Kinetic energy of the sphere is $\frac{5}{6}\, mv^2$

B

Kinetic energy of the sphere is $\frac{4}{5}\, mv^2$

C

Angular momentum of the sphere about a fixed point on ground is $\frac{8}{3}\, mvR$

D

Angular momentum of the sphere about a fixed point on ground is $\frac{14}{5}\, mvR$

Solution

$L=I \omega+2 m v R$

$L=\left(\frac{2}{3} M R^{2}\right) \times \frac{V}{R}+2 m v R \Rightarrow L=\frac{8}{3} m v R$

Standard 11

Physics

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