RRB Technician Grade 1 Model Paper 1

Concept:Momentum of a body is directly proportional to the square root of its kinetic energy.So, if kinetic energy becomes $n$ times, momentum becomes $\sqrt{n}$ times.Explanation:The relation between kinetic energy $K$ and momentum $P$ is given by:$$K = \frac{P^2}{2m}$$Rearranging this equation, we get:$$P = \sqrt{2mK}$$This clearly shows that $P \propto \sqrt{K}$.Given that the new kinetic energy is 36 times the original value:$$K_f = 36K_i$$Therefore, the new momentum becomes:$$P_f = \sqrt{2m \times 36K_i}$$$$P_f = 6\sqrt{2mK_i}$$$$P_f = 6P_i$$Now, the percentage increase in momentum is calculated as:$$\text{Percentage increase} = \frac{P_f - P_i}{P_i} \times 100\%$$Substituting $P_f = 6P_i$:$$= \frac{6P_i - P_i}{P_i} \times 100\%$$$$= \frac{5P_i}{P_i} \times 100\%$$$$= 500\%$$Answer:The percentage increase in momentum of the body is $\mathbf{500\%}$.Correct option: A. 500%