Work Energy and Power - Result Question 28

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31. If the momentum of a body is increased by $50 %$, then the percentage increase in its kinetic energy is

======= ####31. If the momentum of a body is increased by $50 %$, then the percentage increase in its kinetic energy is

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/work-energy-and-power/work-energy-and-power—result-question-28.md (a) $50 %$

(b) $100 %$

(c) $125 %$

(d) $200 %$

[1995]

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Answer:

Correct Answer: 31. (c)

Solution:

  1. (c) Initial momentum $(p_1)=p$; Final momentum $(p_2)=1.5 p$ and initial kinetic energy $(K_1)=K$.

Kinetic energy $(K)=\frac{p^{2}}{2 m} \propto p^{2}$

or, $\frac{K_1}{K_2}=(\frac{p_1}{p_2})^{2}=(\frac{p}{1.5 p})^{2}=\frac{1}{2.25}$

or, $K_2=2.25 K$.

Therefore, increase in kinetic energy is $2.25 K-K=1.25 K$ or $125 %$.