Q116 / 150 · MHT CET 2022 (05 Aug Shift 1) · Physics

A $4 \mathrm{~kg}$ mass and a $1 \mathrm{~kg}$ mass are moving with equal energies. The ratio of the magnitude of their linear momenta is

  • Correct answer
    A
    $2: 1$
  • B
    $4: 1$
  • C
    $1: 2$
  • D
    $1: 1$

Solution

The correct option is (A). Kinetic Energy $\mathrm{K}$ and momentum $p$ are related as: $\mathrm{K}=\frac{\mathrm{p}^2}{2 \mathrm{~m}}$ Therefore, $P=\sqrt{2 K m}$ The ratio of momentum for $4 \mathrm{~kg}$ mass and $1 \mathrm{~kg}$ mass moving with equal kinetic energy $\mathrm{K}$ is $\frac{\mathrm{p}_{4 \mathrm{~kg}}}{\mathrm{p}_{1 \mathrm{~kg}}}=\sqrt{\frac{2 \mathrm{~K}(4 \mathrm{~m})}{2 \mathrm{~K}(\mathrm{~m})}}=\frac{2}{1}$

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

Relevant Questions