The momentum of a body is increased by 50%. The percentage increase in the kinetic energy of the body is ______%
Correct Answer: 125
Solution and Explanation
Step 1: Relation between kinetic energy and momentum - Kinetic energy \[ K = \frac{P^2}{2m}, \] where \(P\) is momentum and \(m\) is mass.
Step 2: Calculate new kinetic energy - Initial momentum \(P_1\), kinetic energy \[ K_1 = \frac{P_1^2}{2m}. \] New momentum \[ P_2 = P_1 + 0.5P_1 = 1.5P_1. \] New kinetic energy \[ K_2 = \frac{P_2^2}{2m} = \frac{(1.5P_1)^2}{2m} = \frac{2.25P_1^2}{2m} = 2.25K_1. \]
Step 3: Calculate percentage increase in kinetic energy - Percentage increase is given by: \[ \frac{K_2 - K_1}{K_1} \times 100 = \frac{2.25K_1 - K_1}{K_1} \times 100 = 125\%. \]
Final Answer: The percentage increase in kinetic energy is 125%.
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