Question

The kinetic energy of a body is increased by 21%. The percentage increase in its linear momentum is:

• A. 10%
• B. 11%
• C. 1%
• D. 20%
• E. 21%

Hint:

Kinetic energy depends on velocity squared, while momentum is directly proportional to velocity.

Answer 1

The Correct Option is A

Kinetic energy is: \[ K = \frac{1}{2} m v^2 \] A 21% increase in kinetic energy means: \[ K_{\text{new}} = 1.21 K \] Since \( v_{\text{new}}^2 = 1.21 v^2 \), taking the square root: \[ v_{\text{new}} = \sqrt{1.21} v \approx 1.1 v \] Momentum is \( p = mv \), so an increase in velocity by 10% means momentum also increases by 10%.