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Question

A metal ball falls from a height of 1 m on to a steel plate and jumps upto a height of 81 cm. Find the coefficient of restitution of the ball material.

A
0.2
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B
9
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C
0.9
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D
90
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Solution

The correct option is D 0.9
Let
u1=Velocity of ball before collision
v1=Velocity of ball after collision
u2=Velocity of plate before collision=0
v2=Velocity of plate after collision=0
The coefficient of restitution(e) is given by,
e=RelativevelocityofballaftercollisionRelativevelocityofballbeforecoliision
e=v1v2u1u2
e=v10u10=v1u1
Using v21=2gh1v1=2gh1
Using u21=2gh2u1=2gh2
e=2gh12gh2=h1h2
Here, h1=100cm,h2=90cm
e=h2h1=81100=0.9

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