A circular hoop of mass m and radius r

Asked by admin @ 23/08/2021 in Physics viewed by 340 People

A circular hoop of mass m and radius R rests flat on a horizontal frictionless surface. A bullet also of mass m, and moving with a velocity v, strikes the hoop and gets embedded in it. The thickness of the hoop is much smaller than R. The angular velocity with which the system rotates after the bullet strikes the hoop is

Answered by admin @ 23/08/2021

centre of mass of the loop - bullet system is R/2 from centre of loop.

By momentum conservation :

mv=2mVcm

Vcm=v/2

Applying angular momentum conservation about the centre of mass.

MVR/2=Iw

I for ring =mr2+m(r/2)2

I of bullet =m(r/2)2

moment of inertia of the system I=6mR2/4

=3/2mR2

mvR2=3/2mR2w

w=v/3R

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