Question

If the momentum of a body is increased by $100\%$, then the percentage increase in the kinetic energy is

• A. $150\%$
• B. $200\%$
• C. $225\%$
• D. $300\%$

Answer 1

The correct option is D

$300\%$

Step 1: Given

Initial momentum, $P$

Increase in momentum,

$$\begin{gathered} P\text{'}=P+100\%\left(P\right) \\ =P+\frac{100}{100}P \\ =2P \end{gathered}$$

Step 2: Determine the KE

Kinetic energy is given by,

$KE=\frac{P^2}{2m}$ (where P is the momentum and m is the mass)

Step 3: Determine the new KE

After the momentum is increased by $100\%$,

$$\begin{gathered} KE=\frac{P{\text{'}}^2}{2m} \\ =\frac{{\left(2P\right)}^2}{2m} \\ =\frac{4P^2}{2m} \\ =\frac{P^2}{2m}+\frac{3P^2}{2m} \\ =KE+3KE \\ =KE+\frac{300}{100}KE \\ =KE+300\%KE \end{gathered}$$

Therefore, option D is the correct option.