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QJEEM11Phdb4a: JEE Main 2011 Physics - Class 11 JEEM11Phdb4a Solution: Two bodies of masses and are placed at a distance The…

Two bodies of masses mm and 44 mm are placed at a distance r.r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

Multiple Choice Options

  • A −4Gmr- {{4Gm} \over r}
  • B −6Gmr- {{6Gm} \over r}
  • C −9Gmr- {{9Gm} \over r}
  • D zero

Step-by-Step Verified Solution

Let the gravitational field at P,P, distant xx from mass m,m, be zero.
AIEEE 2011 Physics - Gravitation Question 177 English Explanation
∴\therefore Gmx2=4Gm(r−x)2{{Gm} \over {{x^2}}} = {{4Gm} \over {{{\left( {r - x} \right)}^2}}}

⇒4x2=(r−x)2\Rightarrow 4{x^2} = {\left( {r - x} \right)^2}

⇒2x=r−x\Rightarrow 2x = r - x

⇒x=r3\Rightarrow x = {r \over 3}

Gravitational potential at point P,P,

V=−Gmr3−4Gm2r3=−9GmrV = - {{Gm} \over {{r \over 3}}} - {{4Gm} \over {{{2r} \over 3}}} = -{{9Gm} \over r}

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