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Angular Analogue of Linear Momentum

If momentum o...

Question

If momentum of a body increases by $50 %$ by what $%$ its K.E. change?

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Solution

Let the initial momentum be $P_{i} = P$
Final momentum $P_{f} = 1.5 P$
Initial kinetic energy $K . E_{i} = \frac{p^{2}}{2 m}$
Final kinetic energy $K . E_{f} = \frac{p_{f}^{2}}{2 m} = \frac{(1.5 P)^{2}}{2 m} = 2.25 K . E_{i}$
Percentage increase in kinetic energy $\frac{K . E_{f} - K . E_{i}}{K . E_{i}} \times 100 = \frac{2.25 - 1}{1} \times 100 = 125$ %

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