1. Let the initial momentum and kinetic energy of the body be $p$ and $K$ respectively.

2. We use the relation between kinetic energy and momentum: $K = \frac{p^2}{2m}$ where $m$ is the mass of the body.

3. Since mass remains constant, $K \propto p^2$ So, $p \propto \sqrt{K}$

4. According to the question, the kinetic energy becomes $36$ times the original value: $K' = 36K$ Therefore, $p' = \sqrt{36}\,p = 6p$

5. Thus, the new momentum is $6$ times the original momentum. The increase in momentum is: $\Delta p = p' - p = 6p - p = 5p$

6. Percentage increase in momentum: $\frac{\Delta p}{p} \times 100 = \frac{5p}{p} \times 100 = 500\%$

7. Checking options:

• A: $60\%$ ❌
• B: $500\%$ ✅
• C: $6\%$ ❌
• D: $600\%$ ❌

Hence, the correct answer is B: $500\%$.