1. Write the relation between kinetic energy and momentum

For a body of mass $m$, $K = \frac{p^2}{2m}$ where $K$ is kinetic energy and $p$ is momentum.

2. Compare initial and final kinetic energies

Let the initial kinetic energy be $K_i$ and initial momentum be $p_i$. Let the final kinetic energy be $K_f$ and final momentum be $p_f$.

Given: $K_f = 4K_i$

Using $K \propto p^2$ for constant mass, we get: $\frac{K_f}{K_i} = \frac{p_f^2}{p_i^2}$

So, $4 = \frac{p_f^2}{p_i^2}$ $\Rightarrow \frac{p_f}{p_i} = 2$

Thus, $p_f = 2p_i$

3. Find the percentage change in momentum

Change in momentum: $\Delta p = p_f - p_i = 2p_i - p_i = p_i$

Percentage change: $\frac{\Delta p}{p_i} \times 100 = \frac{p_i}{p_i} \times 100 = 100\%$

4. Evaluate options

• A: $100\%$ ✅
• B: $200\%$ ❌
• C: $300\%$ ❌
• D: $400\%$ ❌

Therefore, the correct answer is A.