Question

The kinetic energy of a body decreases by 36%. The decrease in its momentum is

Moderate

Solution

$P = \sqrt{2 mE} ∴ P \propto \sqrt{E}$
In given problem K.E. becomes 64% of the original value.
$\frac{P_{2}}{P_{1}} = \sqrt{\frac{E_{2}}{E_{1}}} = \sqrt{\frac{64 E}{100 E}} = 0 .8 \Rightarrow P_{2} = 0 .8 P$
$∴ P_{2} = 80 %$ of the original value.
i.e. decrease in momentum is 20%.

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