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Question

A spherical body of radius 'R' rolls on a horizontal surface with linear velocity 'v'. Let L1 and L2 be the magnitudes of angular momenta of the body about centre of mass and point of contact P. Then,

A
L2=2L1 ; if radius of gyration K = R
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B
L2=2L1 ; for all cases
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C
L2>2L1 ; if radius of gyration K < R
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D
L2>2L1 ; if radius of gyration K > R
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Solution

The correct option is D L2>2L1 ; if radius of gyration K > R
L1=Iw=MK2w.....(1)
L2=Iw+MRv
=MK2w+MR(wR) (as v = Rw)
=Mw(K2+R2)...(2)
From equations (1) and (2), we can see that
L2=2L1
when K = R
and L2>2L1
when K > R

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