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JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Physics
Chapter
Work, Power and Energy

JEE Main 2024 · 4 April · Morning Shift · Physics · Work, Power and Energy

If a rubber ball falls from a height h and rebounds upto the height...

If a rubber ball falls from a height hh and rebounds upto the height of h/2h / 2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

Options

  1. A50%,2gh50 \%, \sqrt{2 \mathrm{gh}}
  2. B50%,gh50 \%, \sqrt{\mathrm{gh}}
  3. C40%,2gh40 \%, \sqrt{2 \mathrm{gh}}
  4. D50%,gh250 \%, \sqrt{\frac{\mathrm{gh}}{2}}

Correct answer

A. 50%,2gh50 \%, \sqrt{2 \mathrm{gh}}

Step-by-step solution

 Velocity just before collision =2gh Velocity just after collision =2g(h2)∴ΔKE=12m(2gh)−12mgh=12mgh∴% loss in  energy =ΔKEKEi×100=12mgh12mg2h×100=50%\begin{aligned} & \text{ Velocity just before collision }=\sqrt{2 \mathrm{gh}} \\ & \text{ Velocity just after collision }=\sqrt{2 \mathrm{ g}\left(\frac{\mathrm{h}}{2}\right)} \\ & \therefore \Delta \mathrm{KE}=\frac{1}{2} \mathrm{ m}(2 \mathrm{gh})-\frac{1}{2} \mathrm{mgh} \\ & =\frac{1}{2} \mathrm{mgh} \\ & \therefore \% \text{ loss\text{ in } energy } \\ & =\frac{\Delta \mathrm{KE}}{\mathrm{KE}_{\mathrm{i}}} \times 100=\frac{\frac{1}{2} \mathrm{mgh}}{\frac{1}{2} \mathrm{mg} 2 \mathrm{ h}} \times 100=50 \% \end{aligned}
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