Question 390: Gravitation

Question

Two bodies of mass $$m$$ and $$9 m$$ 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) :

Accepted Answer

Position of Neutral point (Zero Gravitational Field)
$$r_{1}=\frac{\sqrt{m_{1}} R}{\sqrt{m_{1}}+\sqrt{m_{2}}}=\frac{\sqrt{m} R}{\sqrt{m}+\sqrt{9 m}}=\frac{R}{4}$$
$$\mathrm{r}_{2}=\mathrm{R}-\mathrm{R} / 4=3 \mathrm{R} / 4$$
Now Gravitational potential at point $$\mathrm{P}$$
$$
\begin{aligned}
& V_{P}=-\frac{G M}{R / 4}-\frac{9(\mathrm{GM})}{3 \mathrm{R} / 4} \
& =\frac{-16 \mathrm{GM}}{\mathrm{R}}
\end{aligned}
$$

Answer

$$-\frac{12 G m}{R}$$

Answer

$$-\frac{16 G m}{R}$$

Answer

$$-\frac{20 G m}{R}$$

Answer

$$-\frac{8 G m}{R}$$

Gravitation

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

Choose the correct answer: