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%. $
