A ball falls on the ground from a height of 2.0m and rebounds up to a height of 1.5m. Find the coefficient of restitution for the collision of the ball with the ground. Take g=10m/s2.
A
12
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B
√32
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C
1
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D
0
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Solution
The correct option is B√32
Velocity of ball just before collision with ground v1=√2gh1 where h1=2m ⇒v1=√2×10×2=√40m/s Let the velocity of ball just after collision with ground be v2 upwards, and it reaches a maximum height of h2=1.5m (where v=0)
Considering downward direction as +ve, v2=u2+2as where s=−h2,u=−v2,a=+g 02=(−v2)2+2×(+g)×(−h2) ⇒v2=√2gh2=√2×10×1.5 ∴v2=√30m/s
For the collision of ball with ground, we can assume ground to be stationary, Speed of approach=v1 Speed of separation=v2
Coefficient of restitution, e=Speed of separationSpeed of approach ⇒e=v2v1=√30√40 ∴e=√34=√32