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JEE Main 20246 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Evening Shift
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

JEE Main 2024 · 6 April · Evening Shift · Physics · Center of Mass, Momentum and Collision

When kinetic energy of a body becomes 36 times of its original...

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:

Options

  1. A6%6 \%
  2. B600%600 \%
  3. C60%60 \%
  4. D500%500 \%

Correct answer

D. 500%500 \%

Step-by-step solution

Kinetic energy (K)=P22m⇒P=2mK(K)=\frac{P^2}{2 m} \Rightarrow \mathrm{P}=\sqrt{2 \mathrm{mK}}If Kf=36KiK_f=36 K_i So, Pf=6Pi\mathrm{P}_{\mathrm{f}}=6 \mathrm{P}_{\mathrm{i}}% increase in momentum =Pf−PiPi×100%=6Pi−PiPi×100%=500%\begin{aligned} \% \text{ increase in momentum } & =\frac{\mathrm{P}_{\mathrm{f}}-\mathrm{P}_{\mathrm{i}}}{\mathrm{P}_{\mathrm{i}}} \times 100 \% \\ & =\frac{6 \mathrm{P}_{\mathrm{i}}-\mathrm{P}_{\mathrm{i}}}{\mathrm{P}_{\mathrm{i}}} \times 100 \% \\ & =500 \% \end{aligned}$$
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