Work Energy And Power Question 45

Question: If the linear momentum is increased by 50%, the kinetic energy will increase by [CPMT 1983; MP PMT 1994; MP PET 1996, 99; UPSEAT 2001]

Options:

A) 50%

B) 100%

C) 125%

D) 25%

Show Answer

Answer:

Correct Answer: C

Solution:

Let $ P_1=P $ , $ P_2=P_1+50% $ of $ P_1 $ = $ P_1+\frac{P_1}{2}=\frac{3P_1}{2} $

$ E\propto P^{2} $

therefore $ \frac{E_2}{E_1}={{( \frac{P_2}{P_1} )}^{2}}={{( \frac{3P_1/2}{P_1} )}^{2}}=\frac{9}{4} $

therefore $ E_2=2.25E $

$ =E_1+1.25E_1 $

$ E_2=E_1+125$ % $\text{of }E_1 $

i.e. kinetic energy will increase by 125%.



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