Q103 / 150 · MHT CET 2020 (15 Oct Shift 1) · Physics

Two masses of 1 gram and 4 gram are moving with equal kinetic energy. The ratio of the magnitudes of their momenta is

  • A
    $4: 1$
  • B
    $\sqrt{2}: 1$
  • Correct answer
    C
    $1: 12$
  • D
    $1: 16$

Solution

Kinetic energy $\mathrm{K}=\frac{\mathrm{p}^{2}}{2 \mathrm{~m}}$ Two masses are given as- $\mathrm{m}_{1}=1 \mathrm{gm}$ and $\mathrm{m}_{2}=4 \mathrm{gm}$ But $\mathrm{K}_{1}=\mathrm{K}_{2}$ $\therefore \frac{\mathrm{p}_{1}^{2}}{2 \mathrm{~m}_{1}}=\frac{\mathrm{P}_{2}^{2}}{2 \mathrm{~m}_{2}}$ Or $\frac{\mathrm{P}_{1}^{2}}{2(1)}=\frac{\mathrm{P}_{2}^{2}}{2(4)}$ $\Longrightarrow \mathrm{P}_{1}: \mathrm{P}_{2}=1: 2$

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

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