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Question

# Two unequal point masses M and m, are a distance d apart and revolve with same angular speed about their common center of mass. The ratio of their angular momentum about their center of mass LMLm is :

A
(Mm)2
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B
Mm
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C
mM
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D
(mM)2
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Solution

## The correct option is C mM Two particles A and B having mass M and m , respectively. Let, both A and B revolves about C with angular speed ω . Coordinates of B=(d,0) Thus, coordinates of centre of mass (C) is (M×0+m×dM+m,0)=(mM+md,0) Therefore, LMLm=IM⋅CMIm⋅Cm=IMIm(∵Cm=ωm=ω)∴LMLm=[M⋅(mm+M)2d2][m⋅(d−mdm+M)2]=mM

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