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JEE Main 20253 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
3 April
Shift
Morning Shift
Subject
Physics
Chapter
Work, Power and Energy

JEE Main 2025 · 3 April · Morning Shift · Physics · Work, Power and Energy

A particle is released from height S above the surface of the...

A particle is released from height SS above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

Options

  1. AS2,3gS2\frac{\mathrm{S}}{2}, \sqrt{\frac{3 \mathrm{gS}}{2}}
  2. BS2,3gS2\frac{\mathrm{S}}{2}, \frac{3 \mathrm{gS}}{2}
  3. CS4,3gS2\frac{\mathrm{S}}{4}, \frac{3 \mathrm{gS}}{2}
  4. DS4,3gS2\frac{\mathrm{S}}{4}, \sqrt{\frac{3 \mathrm{gS}}{2}}

Correct answer

D. S4,3gS2\frac{\mathrm{S}}{4}, \sqrt{\frac{3 \mathrm{gS}}{2}}

Step-by-step solution

<br/>V2=0+2 g( S−x)V2=2 g( S−x)<br/>\begin{aligned}<br/>& \mathrm{V}^2=0+2 \mathrm{~g}(\mathrm{~S}-\mathrm{x}) \\ & \mathrm{V}^2=2 \mathrm{~g}(\mathrm{~S}-\mathrm{x})<br/>\end{aligned}
At B, Potential energy =mgx=m g x
<br/>mgx=3×12mv2gx=32×2 g( S−x)4x=Sx=S4<br/>\begin{aligned}<br/>& \mathrm{mgx}=3 \times \frac{1}{2} \mathrm{mv}^2 \\ & \mathrm{gx}=\frac{3}{2} \times 2 \mathrm{~g}(\mathrm{~S}-\mathrm{x}) \\ & 4 \mathrm{x}=\mathrm{S} \\ & \mathrm{x}=\frac{\mathrm{S}}{4}<br/>\end{aligned}
⇒V=2 g×3 S4=3gS2\Rightarrow \mathrm{V}=\sqrt{2 \mathrm{~g} \times \frac{3 \mathrm{~S}}{4}}=\sqrt{\frac{3 \mathrm{gS}}{2}}
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