Question

If the linear momentum is increased by $50\%$, then kinetic energy will be increased by

• A. $50\%$
• B. $20\%$
• C. $125\%$
• D. None of these

Answer 1

The correct option is C

$125\%$

Step 1: Given

Initial linear momentum, $P$

Momentum after increasing, $$\begin{gathered} P\text{'}=P+50\%P \\ =P+0.5P \\ =1.5P \end{gathered}$$

Step 2: Determine the kinetic energy

The 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 kinetic energy

$$\begin{gathered} KE\text{'}=\frac{P{\text{'}}^2}{2m} \\ =\frac{{(1.5P)}^2}{2m} \\ =\frac{2.25P^2}{2m} \\ =\frac{P^2}{2m}+1.25\frac{P^2}{2m} \\ =KE+1.25KE \\ =KE+125\%KE \end{gathered}$$

Therefore, option C is the correct option.