Q.

A uniform bar of length 6a& mass 8m lies on a smooth horizontal table. Two point masses 'm& 2m' moving in the same horizontal plane with speeds 2v & 'v' respectively strike the bar as shown & stick to the bar after collision then

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a

Velocity of the centre of mass is zero

b

Angular velocity about centre of mass= v5a

c

Total kinetic energy just after collision is 35mv2

d

Total kinetic energy just after collision is 32mv2

answer is A, B, C.

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Detailed Solution

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From conservation of linear momentum

2mV2mV=(11m)VVcm=0
About C, from conservation of angular momentum

(2mV)a+m(2V)2a+0=8m[6a]212+2ma2+m(2a)2ωω=v5a

KE=12Isystem ω2=1230ma2v225a2=35mv2

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