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A small sphere of mass m =1 kg is moving...

A small sphere of mass `m =1 kg` is moving with a velocity `(4hati-hatj) m//s`. it hits a fixed smooth wall and rebounds with velocity `(hati + 3hatj) m//s`. The coefficient of restitution between the sphere and the wall is `n//16`. Find the value of `n`.

Text Solution

Verified by Experts

The correct Answer is:
9
`intNdt=1[(hati+3hatj)-(4hati-hatj)]=-3hati=4hatj`
Component of `4hati-hatj` along `-3hati+3hatj`
`=(-12-4)/25(-3hati=4hatj)=-16/25(-3hati+4hatj)`

Speed of approach `=16/15sqrt(25)=16/5`
component of `hati+3hatj` along `-3hati+4hatj` is `(-3+12)/25(-3hati+4hatj)`
speed of seperation of `=9/5`
speed of separation of `=exx` speed of approach
`e=9/16 n=9`
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