A light body of momentum ' $\mathrm{P}_{\mathrm{L}}$ ' and a heavy body of momentum '…

A light body of momentum ' $\mathrm{P}_{\mathrm{L}}$ ' and a heavy body of momentum ' $\mathrm{P}_{\mathrm{H}}$ ', both have the same kinetic energy, then
  1. $\mathrm{P}_{\mathrm{L}} \gt \mathrm{P}_{\mathrm{H}}$
  2. $\mathrm{P}_{\mathrm{H}} \gt \mathrm{P}_{\mathrm{L}}$
  3. $P_L=P_H$
  4. Always $\mathrm{P}_{\mathrm{H}}=2 \mathrm{P}_{\mathrm{L}}$

Solution

$\mathrm{K}_{\mathrm{H}}=\mathrm{K}_{\mathrm{L}} \Rightarrow \frac{\mathrm{P}_{\mathrm{H}}^2}{2 \mathrm{~m}_{\mathrm{H}}}=\frac{\mathrm{P}_{\mathrm{L}}^2}{2 \mathrm{~m}_{\mathrm{L}}} \Rightarrow \frac{\mathrm{m}_{\mathrm{H}}}{\mathrm{m}_{\mathrm{L}}}=\left(\frac{\mathrm{P}_{\mathrm{H}}}{\mathrm{P}_{\mathrm{L}}}\right)^2$
As $m_H \gt m_L \Rightarrow P_H \gt P_L$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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