First slide

Kinetic energy

Question

Kinetic energy of a particle is increased by 4 times. What will be the relation between initial and final
momentum? [JIPMER 2018]

Easy

A

$p_{2} = 2 p_{1}$
B

$p_{2} = p_{1} / 2$
C

$p_{2} = p_{1}$
D

$p_{2} = 4 p_{1}$

Solution

Relation between kinetic energy and momentum is
$p_{1} = \sqrt{2 m K_{1}}$
$∵$ Kinetic energy is increased by 4 times, then $K_{2} = 4 K_{1}$
Hence, $p_{2} = \sqrt{2 m K_{2}} = \sqrt{2 m (4 K_{1})}$
$p_{2} = 2 \sqrt{2 m K_{1}} or p_{2} = 2 p_{1}$

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