Angular momentum of a rigid body of mass m about an axis is n times linear momentum (P) of body. Tot

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6.System of Particles and Rotational Motion

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The angular momentum of a rigid body of mass m about an axis is $n$ times the linear momentum $(P)$ of the body. Total kinetic energy of the rigid body is

A

$\frac{ P ^2\left[1+ n ^2\right]}{2 m }$

B

$\frac{ n ^2 P ^2}{2 m }$

C

$n ^2 P ^2 \times 2 m$

D

$\frac{ P ^2}{2}\left(\frac{ n ^2}{ I }+\frac{1}{ m }\right)$

(NEET-2017)

Solution

$L = nP$

$KE = KE _{ R }+ KE _{ T }$

$=\frac{ L ^2}{2 I }+\frac{ P ^2}{2 m }$

$=\frac{ n ^2 P ^2}{2 I }+\frac{ P ^2}{2 m }$

$=\frac{ P ^2}{2}\left(\frac{ n ^2}{ I }+\frac{1}{ m }\right)$

Standard 11

Physics

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