Question

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CONTUA
A uniform rod of length l and mass 4m lies on a frictionless horizontal surface on which it is free to
move anyway. A ball of mass m moving with speed v as shown in figure.collides with the rod at
one of the ends. If ball comes to rest immediately after collision then find out angular velocity w of
rod just after collision.​

Answer 1

Answer:

Let us choose the origin of the system at the centre of mass of the rod AB. Thus, Initial angular momentum L

i

=mvL/2, since the rod is not moving. After collision, the particle comes to rest and hence final angular momentum is L

f

=(4m)(L

2

/12)ω

Since no torques are acting on the system, angular momentum is conserved mv(L/2)=4m(L

2

/12)ω. Solving, we get, ω=3V/2L