Question

Two bodies having masses in the ratio 1:3 have equal linear momentum. Their respective kinetic energies are in the ratio:

• A. 3:1
• B. 1:2
• C. 1:3
• D. 4:1
• E. 2:1

Hint:

For equal momentum, the lighter body always has higher kinetic energy.

Answer 1

The Correct Option is A

Step 1: Concept
Kinetic energy $K$ in terms of momentum $P$ is $K = \frac{P^2}{2m}$.

Step 2: Analysis
Since momentum $P$ is equal for both, $K \propto \frac{1}{m}$. $\frac{K_1}{K_2} = \frac{m_2}{m_1}$.

Step 3: Calculation
Given $m_1:m_2 = 1:3$, therefore $K_1:K_2 = 3:1$. Final Answer: (A)