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# Ques no 64

Asked by chandanbr6004 26th November 2017, 10:19 AM
Answered by Expert
Answer:

Force balance: -  mg = R1+µR2

Normal force R2 is unbalanced and makes the sphere to move right to left.

Torque due to the friction force µR2 retarding the circular motion.

Hence µR2×r = I α = (2/5) mr2×α ……………………………(1)

I is Mom. Of Inertia and α is angular retardation

Substitute for µ( µ = 1/5 )and simplify to get

R2 = 2mrα …………………………………………………………(2)

Let the unbalanced horizontal force R2 changes the linear velocity from v to V during the contact time t

Then R2 = m(V-v)/t………………………………………..(3)

From (2)and (3)  m(V-v)/t = -2mrα

Negative sign on RHS is due to retardation

After simplification we get   (V-v) = -2rαt……………(4)

If initial angular velocity is ω and if angular velocity is zero after contact time t, then we can write

0 = ω – αt or ω = αt

Substitute for αt in equation (4) to get (V-v) = -2rω = -2v

Hence V = -v (negative sign indicates sphere moving from right to left)

If we take the magnitude of velocity immediately after collision, |V| = v

Answered by Expert 30th November 2017, 2:48 PM
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