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Question

Case 1: A ball is made to strike a block at a speed of v m/s.
Case 2: The same ball is again made to strike the same block with the speed halved.
What will be the relation between the kinetic energies in both the cases?

A
2KE1 = KE2
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B
2KE1 = 2KE2
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C
KE1 = 4KE2
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D
4KE1 = KE2
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Solution

The correct option is C KE1 = 4KE2

Kinetic energy of a body is given as,

K.E = 12mv2

Let,
Mass of body = m kg
Velocity of body = v m/s

Given:
Velocity in case 2 =12×Velocity in case 1

v2=12×v1

Now, KE1=12mv21

and KE2=12mv22

Substituting the values for v1 and v2 in the equation for KE,

We get, KE2=14KE1

4KE2=KE1

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