Question

The linear momentum of a body is increased by 10 %. What is the percentage change in its kinetic energy?

• A. 15%
• B. 17%
• C. 21%
• D. 27%

Answer 1

Answer: (C)

21%

As momentum is mass x velocity.

So $10\%$ increase in momentum means$10\%$ increase in velocity.

So, if initial velocity is $v$, then new velocity is $1.1v$

Thus initial K.E. $K_i=m{v}^2/2$.

Final K.E. $K_f=m(1.1v{)}^2/2=1.21m{v}^2/2=1.21K_i$

Change in K.E. is $(K_f-K_i)/K_i=0.21=21\%$