2023 GravitationGravitational Potential and Field Medium Question 10 of 66 in Gravitation

Two bodies of mass $m$ and $9m$ are placed at a distance $R$. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ($G$ = gravitational constant):

A $-\frac{20Gm}{R}$
B $-\frac{8Gm}{R}$
C $-\frac{12Gm}{R}$
D $-\frac{16Gm}{R}$

The answer is D.

Solution

Field is zero at $x=\frac{R}{4}$ from $m$; potential there is $-\frac{16Gm}{R}$.

Let the gravitational field be zero at a distance $x$ from the mass $m$. $\frac{Gm}{x^2}=\frac{G9m}{(R-x)^2}\Rightarrow R-x=3x$ or $x=\frac{R}{4}$ Gravitational potential at $\frac{R}{4}$: $=-\frac{Gm}{R/4}-\frac{G9m}{3R/4}$ $=-\frac{4Gm}{R}-\frac{12Gm}{R}=-\frac{16Gm}{R}$

Concept neutral point of two masses

Gravitation in past papers

66 questions from this chapter have appeared across 26 exam years.