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Question

A particle is moving in translatory motion. If momentum of the particle decreases by 10%, kinetic energy will decrease by :

A
10%
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B
5%
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C
20%
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D
19%
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Solution

The correct option is D 19%
According to question,
Momentum of the particle decrease by 10%.
As we know, momentum of particle
p=2mK
pK and p1K1
Final momentum, p1=p10p100
p1=90p100
So, pp1=KK1(10090)2=KK1
100008100=KK1
81100=K1K
Decreasing both sides from 1,
181100=1K1K
10081100=KK1K
KK1K=19100
Change in kinetic energy
(KK1K)×100=(19100)×100=19%

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