MHT CET · Physics · Work Power Energy
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
- A \(2: 1\)
- B \(4: 1\)
- C \(1: 2\)
- D \(1: 1\)
Answer & Solution
Correct Answer
(A) \(2: 1\)
Step-by-step Solution
Detailed explanation
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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