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A pariticle of mass m is performing ...

A pariticle of mass m is performing a U.C .M along a circular path of radius r. Its angular momentum abount the axis of rotation ( axis of the circle ( is L. What is the kinetic energy of the pariticle ?

A

`(1)/(2) (L^(2))/(mr^(2))`

B

`(2L ^(2))/(mr^(2))`

C

`(L^(2))/(mr^(2))`

D

`(2L^(2))/(3mr^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
For the revolving particle , `L= I omega `
` therefore L= mr ^(2) xx(v )/(r ) = m vr `
` therefore v= (L )/(mr)`
`and K.E. =(1)/(2) mv^(2) =(1)/(2) m. (L^(2))/(m^(2)r^(2))`
`=(1)/(2) (L^(2))/(mr ^(2))`
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