Question

If two bodies one light and other heavy have equal kinetic energies, which one has a greater momentum?

• A. Heavy body
• B. Light body
• C. Both have equal momentum
• D. It depends on the actual velocities

Hint:

For equal kinetic energy, momentum is proportional to \( \sqrt{m} \). Lighter bodies have greater momentum.

Answer 1

The Correct Option is B

Given: Both bodies have equal kinetic energy.
Kinetic energy is defined as: \[ KE = \frac{1}{2}mv^2 \] Momentum is defined as: \[ p = mv \] From kinetic energy, we can solve for momentum: \[ p = mv = \sqrt{2m \cdot KE} \] So, \[ p \propto \sqrt{m} \] This implies that for equal kinetic energy, a lighter mass will have greater velocity, and therefore higher momentum.
Hence, the light body has greater momentum than the heavy one under the condition of equal kinetic energy.