Question:
If the momentum of a body is increased by 100%, then the percentage increase in the kinetic energy is
If the momentum of a body is increased by 100%, then the percentage increase in the kinetic energy is
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If the momentum of a body is increased by 100%, then the percentage increase in the kinetic energy is
Updated On: Apr 15, 2026
- 150%
- 200%
- 225%
- 300%
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The Correct Option is D
Solution and Explanation
Step 1: Formula
Kinetic Energy ($KE$) and momentum ($p$) are related by: $KE = \frac{p^{2}}{2m}$.
Step 2: Analysis
If momentum increases by 100%, the new momentum $p_{2} = 2p$. $KE_{2} = \frac{(2p)^{2}}{2m} = 4 \times \frac{p^{2}}{2m} = 4KE_{1}$.
Step 3: Percentage Increase
Increase in $KE = KE_{2} - KE_{1} = 4KE_{1} - KE_{1} = 3KE_{1}$. Percentage increase $= 3 \times 100% = 300%$.
Final Answer: (D)
Kinetic Energy ($KE$) and momentum ($p$) are related by: $KE = \frac{p^{2}}{2m}$.
Step 2: Analysis
If momentum increases by 100%, the new momentum $p_{2} = 2p$. $KE_{2} = \frac{(2p)^{2}}{2m} = 4 \times \frac{p^{2}}{2m} = 4KE_{1}$.
Step 3: Percentage Increase
Increase in $KE = KE_{2} - KE_{1} = 4KE_{1} - KE_{1} = 3KE_{1}$. Percentage increase $= 3 \times 100% = 300%$.
Final Answer: (D)
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