JEE Main · 2011 · 10 Apr 2011 · Offline · Gravitation

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Two bodies of masses m and 4 m are placed at a distance r . The gravitational potential at a point on the line joining them where the gravitational field is zero is:

(A) $- \frac{4 G m}{r}$
(B) $- \frac{6 G m}{r}$
(C) $- \frac{9 G m}{r}$ ✓ Correct
(D)zero

Answer: (C)

Solution

The gravitational field vanishes between the masses where the pulls of

m

and

4 m

balance. Measuring a distance

x

from

m

\frac{G m}{x ^{2}} = \frac{G ( 4 m )}{( r - x ) ^{2}}

gives

r - x = 2 x

, so

x = \frac{r}{3}

and the point is

\frac{2 r}{3}

from the heavier mass. The potential is the scalar sum of the two parts,

V = - \frac{G m}{r /3} - \frac{G ( 4 m )}{2 r /3} = - \frac{3 G m}{r} - \frac{6 G m}{r} = - \frac{9 G m}{r}

JEE Main · 2011 · 10 Apr 2011 · Offline · Single correct option

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