Question 213: Gravitation

Question

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:

Accepted Answer

Let the gravitational field at $$P,$$ distant  $$x$$ from mass $$m,$$ be zero.
$$	herefore$$ $${{Gm} \over {{x^2}}} = {{4Gm} \over {{{\left( {r - x} ight)}^2}}}$$
$$ \Rightarrow 4{x^2} = {\left( {r - x} ight)^2}$$
$$ \Rightarrow 2x = r - x$$
$$ \Rightarrow x = {r \over 3}$$
Gravitational potential at point $$P,$$
$$V =  - {{Gm} \over {{r \over 3}}} - {{4Gm} \over {{{2r} \over 3}}} = -{{9Gm} \over r}$$

Answer

$$ - {{4Gm} \over r}$$

Answer

$$ - {{6Gm} \over r}$$

Answer

$$ - {{9Gm} \over r}$$

Answer

zero

Gravitation

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:

Choose the correct answer: