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A point mass m moving with velocity u towards the centre of the disc collides with a disc of mass m and radius r resting on a rough horizontal surface. Its collision is perfectly inelastic. Find angular velocity of system after pure rolling starts. A) 2u/7r B) 7u/2r C) 5u/2r D) 2u/5r
A point mass m moving with velocity u towards the centre of the disc collides with a disc of mass m and radius r resting on a rough horizontal surface. Its collision is perfectly inelastic. Find angular velocity of system after pure rolling starts.
A) 2u/7r
B) 7u/2r
C) 5u/2r
D) 2u/5r
initial linear momentum = mu. final velocity =v and pure rolloing angular velocity=w. let total linear impulse = J, total angular impulse = Jr. linear/angular impulse = change in linear/angular momentum J=mu-2mv Jr= mwr2/2 = mvr/2 J=mv/2= mu-2mv,implies v=2u/5,implies w=2u/5r
initial linear momentum = mu. final velocity =v and pure rolloing angular velocity=w.
let total linear impulse = J, total angular impulse = Jr. linear/angular impulse = change in linear/angular momentum
J=mu-2mv
Jr= mwr2/2 = mvr/2
J=mv/2= mu-2mv,implies v=2u/5,implies w=2u/5r
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