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JEE Main 202311 AprilEvening Shift
Exam
JEE Main
Year
2023
Date
11 April
Shift
Evening Shift
Subject
Physics
Chapter
Electrostatics

JEE Main 2023 · 11 April · Evening Shift · Physics · Electrostatics

If V is the gravitational potential due to sphere of uniform...

If VV is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be:

Options

  1. A43V\dfrac{4}{3}V
  2. BV2\dfrac{V}{2}
  3. CVV
  4. D3V2\dfrac{3V}{2}

Correct answer

D. 3V2\dfrac{3V}{2}

Step-by-step solution

The magnitude of gravitational potential of a solid sphere at a distance rr from the centre is

V=−GM2R3(3R2−r2)V = \dfrac{- GM}{2{R}^{3}} ( 3{R}^{2} - {r}^{2} )

At r=Rr = R, V=−GMRV = \dfrac{- GM}{R}.

At r=0r = 0, V′=−GM2R3(3R2)=−3GM2RV ' = \dfrac{- GM}{2{R}^{3}} ( 3{R}^{2} ) = \dfrac{- 3GM}{2R}

Clearly, V′=3V2V ' = \dfrac{3V}{2}.

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