Question

Two bodies of masses $m$ and $4m$ 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. $-\frac{4Gm}{r}$
• B. $-\frac{6Gm}{r}$
• C. $-\frac{9Gm}{r}$
• D. Zero

Answer 1

The correct option is C $-\frac{9Gm}{r}$

Two masses m and 4m kept at a distance r. Let, gravitation field be zero at P as shown in figure.
$\therefore \frac{G\text{m}}{{\text{x}}^2}=\frac{G\times 4\text{m}}{(\text{r-x}{)}^2}$
$\Rightarrow 4{\text{x}}^2=(\text{r -x}{)}^2$
$\Rightarrow (2\text{x}{)}^2-(\text{r-x}{)}^2=0$
$\Rightarrow 2\text{x = r - x}$
$\Rightarrow \text{x}=\frac{\text{r}}{3}$
Potnetial at point P
$\therefore V_P=-\frac{\text{Gm}}{\text{x}}-\frac{\text{G(4m)}}{\text{r - x}}$
$=-\frac{\text{3Gm}}{\text{r}}-\frac{\text{6 Gm}}{\text{r}}=-\frac{\text{9 Gm}}{\text{r}}$