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Question

A uniform bar of length 6l lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2v and v respectively.strike the bar (as shown in the fig.) and stick to the bar after collision. Total center of mass, c) will be :-
1111203_6a5ded5eff1347aa9e99b4c1c7f693be.png

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Solution

Fext=0

2mv+m×2v+0=(2m+m+8m)vc

vc=0

zext=0

m1v1r1+m2v2r2=(J1+J1+J1)w

2mva+2m(2v)(2a)=

2ma2+m(2a)2+8m×(6a)212w

6mva=30mwa2

w=v5a

E=12Iw2=12(30ma2)(v2a)2

=35mv2


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