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  4. If momentum of a particle increased 30 %, then increase in its kinetic energy is:

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Q. If momentum of a particle increased $30\%$, then increase in its kinetic energy is:

Rajasthan PMTRajasthan PMT 1999

Solution:

Momentum $p \propto \sqrt{E}$
$\frac{p_{1}}{p_{2}} =\sqrt{\frac{E_{1}}{E_{2}}}$
$\frac{p}{p+\frac{3 p}{10}} =\sqrt{\frac{E_{1}}{E_{2}}}$
$\therefore \frac{10}{13} =\sqrt{\frac{E_{1}}{E_{2}}}$
$\therefore \frac{E_{1}}{E_{2}} =\frac{100}{169}$
$\therefore $ increase in kinetic energies $=69 \%$