Work Energy And Power Question 237

Question: If the momentum of a body is increased by 50%, then the percentage increase in its kinetic energy

Options:

A) 50%

B) 100%

C) 125%

D) 200%

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Initial momentum $ ( p_1 )=p, $

Final momentum $ ( p_2 )= 1.5 $ p and initial kinetic energy $ ( K_1 )=K $ .

Kinetic energy $ ( K ) = \frac{p^{2}}{2m}\propto p^{2} $ Or, $ \frac{K_1}{K_2} = {{( \frac{p_1}{p_2} )}^{2}}={{( \frac{p}{1.5p} )}^{2}}=\frac{1}{2.25} $ or, $ K_2=2.25K. $ Therefore, increase in kinetic energy is 2.25 $ KK=1.25Kor125%. $



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