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Question

A body falls from a height 'h' on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficient is 13, the total distance covered by the body before it comes to rest is

A
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B
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C
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D
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Solution

The correct option is B
If a ball is dropped from a height h on a horizontal floor, then it strikes with the floor with a speed.
v0=2gh0 [From v2=u2+2gh]
and it rebounds from the floor with a speed

v1=ev0=e2gh0[Ase=velocity after collisionvelocity before collision]
(1)First height of rebound:h1=v212g=e2h0 h1=e2h0(2)Height of the ball after nth rebound:Obviously, the velocity of ball nth rebound will beTherefore the height after nth rebound will behn=v2n2g=e2nh0 hn=e2nh0
Total distance=h+2e2h+2e4h+=h+2e2h(1+e2+)=h+2e2h1e2=h(1+e21e2)=h1+(13)21(13)2=5h4Hence the correct choice is (b).

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