Q112 / 180 · JIPMER 2018 · Physics

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

  • Correct answer
    A
    $p_2=2 p_1$
  • B
    $p_2=\frac{p_1}{2}$
  • C
    $p_2=p_1$
  • D
    $p_2=4 p_1$

Solution

$\because$ Relation between kinetic energy and momentum is $\mathrm{p}_1=\sqrt{2 \mathrm{mk}_1}$ $\because$ Kinetic energy is increased by 4 times $\therefore \quad \mathrm{k}_2=4 \mathrm{k}_1$ Hence, $\mathrm{p}_2=\sqrt{2 \mathrm{mk}_2}=\sqrt{2 \mathrm{~m}\left(4 \mathrm{k}_1\right)}=2 \sqrt{2 \mathrm{mk}_1}$ or $\quad \mathrm{p}_2=2 \mathrm{p}_1$

Hence, the correct answer is option: 'A'.

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