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STANDARD Physics Gravitational Potential Energy MCQ Question

Type: MCQ-numerical-Medium-Class 11

Q

Question diagram
A

A

B

B

C

C

D

D

Correct Answer

Option A

Detailed Explanation

šŸ§  NEET

Gravitational potential energy of two masses is:

U=āˆ’Gm1m2rU=-\frac{Gm_1m_2}{r}

For 4 particles, there are 6 pairs:

  • 4 pairs along the sides, each separated by ll
  • 2 pairs along the diagonals, each separated by 2ā€‰l\sqrt2\,l

Therefore,

U=4(āˆ’Gm2l)+2(āˆ’Gm22ā€‰l)U=4\left(-\frac{Gm^2}{l}\right) +2\left(-\frac{Gm^2}{\sqrt2\,l}\right) U=āˆ’Gm2l(4+22)U=-\frac{Gm^2}{l}\left(4+\frac{2}{\sqrt2}\right)

Since

22=2\frac{2}{\sqrt2}=\sqrt2 U=āˆ’Gm2l(4+2)\boxed{U=-\frac{Gm^2}{l}(4+\sqrt2)}

āœ… Answer: (A)

āš” Quick Trick: Square ā†’ 4 sides + 2 diagonals

U=āˆ’Gm2(4l+22l)\boxed{U=-Gm^2\left(\frac4l+\frac{2}{\sqrt2l}\right)}

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