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Q. If the linear momentum is increased by $50\%$, then kinetic energy will increase by

AIIMSAIIMS 2016Work, Energy and Power

Solution:

Kinetic energy of the body, $K=\frac{p^{2}}{2 m}$
Since, the mass remains constant
$\therefore K \propto p^{2}$
$\frac{K_{2}}{K_{1}}=\frac{p_{2}^{2}}{p_{1}^{2}}=\left[\frac{150}{100}\right]^{2}=\frac{9}{4}$
$100\left[\frac{K_{2}}{K_{1}}-1\right]=\left(\frac{9}{4}-1\right) \times 100=125 \%$