MHT CET · Physics · Work Power Energy
The kinetic energy of a light body and a heavy body is same. Which one of the following statements is CORRECT?
- A The light body has greater momentum.
- B A body having high velocity has greater momentum.
- C Both bodies have same momentum.
- D The heavy body has greater momentum.
Answer & Solution
Correct Answer
(D) The heavy body has greater momentum.
Step-by-step Solution
Detailed explanation
Kinetic energy,
\(\mathrm{k}=\frac{1}{2} \mathrm{my}^{2}=\frac{(\mathrm{mv})^{2}}{2 \mathrm{~m}}=\frac{\mathrm{p}^{2}}{2 \mathrm{~m}}\)
or \(\mathrm{p}=\sqrt{2 \mathrm{mk}}\) i.e., \(\mathrm{p} \propto=\sqrt{\mathrm{m}}\)
Thus the heavier body has a greater momentum than the lighter one.
\(\mathrm{k}=\frac{1}{2} \mathrm{my}^{2}=\frac{(\mathrm{mv})^{2}}{2 \mathrm{~m}}=\frac{\mathrm{p}^{2}}{2 \mathrm{~m}}\)
or \(\mathrm{p}=\sqrt{2 \mathrm{mk}}\) i.e., \(\mathrm{p} \propto=\sqrt{\mathrm{m}}\)
Thus the heavier body has a greater momentum than the lighter one.
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