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Question

A ball falls from a height of 1 m on the ground and jumps upto a height H. If the coefficient of restitution of the collision is 0.9, then find the value of H.
(Take g=10 m/s2)


Your Answer
A
0.9 m
Correct Answer
B
0.81 m
Your Answer
C
1 m
Your Answer
D
0.71 m

Solution

The correct option is B 0.81 m
Let,
u1= Speed of ball before collision with the surface
v1= Speed of ball after collision with surface
u2= Speed of ground before collision =0
v2= Speed of ground after collision =0
The coefficient of restitution, e=Speed of separationSpeed of approach
Speed of separation =v2(v1)=v1 .....(i)
Speed of approach u1u2=u1 ....(ii)
e=v1u1 ....(iii)
Since ball is dropped from height of 1 m, its speed while just colliding with the ground is
u1=2gh=2×10×1=20 m/s
From eq (iii), we get
0.9=v120
v1=955 m/s

Now, using v2u2=2aH
Initial speed u=v1=955 m/s
Final speed v=0,a=g
0(955)2=2×(10)×H
H=0.81 m

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