Q126 / 160 · TS EAMCET 2023 (12 May Shift 1) · Physics

Two bodies of masses of $1 \mathrm{~g}$ and $4 \mathrm{~g}$ are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

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

Solution

Masses, $\mathrm{m}_1=1 \mathrm{~g} ; \mathrm{m}_2=4 \mathrm{~g}$ Kinetic energy, $K E=\frac{p^2}{2 m}$ $\begin{aligned} & \frac{\mathrm{P}_1^2}{2 \mathrm{~m}_1}=\frac{\mathrm{P}_2^2}{2 \mathrm{~m}_2} \\ & \Rightarrow \frac{\mathrm{P}_1^2}{\mathrm{p}_2^2}=\frac{\mathrm{m}_1}{\mathrm{~m}_2} \\ & \frac{\mathrm{p}_1}{\mathrm{p}_2}=\sqrt{\frac{\mathrm{m}_1}{\mathrm{~m}_2}}=\sqrt{\frac{1}{4}}=\frac{1}{2} \end{aligned}$

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

Relevant Questions