Question

If the linear momentum of a body is increased by 50 %, the Kinetic energy will be increased by

• A. 150 %
• B. 125 %
• C. 50 %
• D. 100 %

Answer 1

Answer: (B)

If the initial momentum is $p_0$, the initial kinetic energy is $K_0=\frac{p_0^2}{2m}$

When momentum is increased by 50 %, the momentum becomes $p=p_0+(p_0\times \frac{50}{100})=\left(3/2\right)p_0$

Now kinetic energy, $K=\frac{p^2}{2m}=\left(9/4\right)\times \left(p_0^2/2m\right)=\left(9/4\right)K_0$

Thus the percentage increased in kinetic energy $=\frac{K-K_0}{K_0}\times 100=\left[\right(9/4)-1]100=125$ %