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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
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Verified Answer
The correct answer is:
$2: 1$
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
$\frac{\mathrm{p}_{4 \mathrm{~kg}}}{\mathrm{p}_{1 \mathrm{~kg}}}=\sqrt{\frac{2 \mathrm{~K}(4 \mathrm{~m})}{2 \mathrm{~K}(\mathrm{~m})}}=\frac{2}{1}$
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
$\frac{\mathrm{p}_{4 \mathrm{~kg}}}{\mathrm{p}_{1 \mathrm{~kg}}}=\sqrt{\frac{2 \mathrm{~K}(4 \mathrm{~m})}{2 \mathrm{~K}(\mathrm{~m})}}=\frac{2}{1}$
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