Question

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

• A. $-\frac{10GM}{r}$
• B. $-\frac{9GM}{r}$
• C. $-\frac{15GM}{r}$
• D. $-\frac{18GM}{r}$

Answer 1

The correct option is B $-\frac{9GM}{r}$


Let $P$ be the null point, which is at a distance $x$ from $m$.
Formula for point of zero intensity,
$x=\frac{{\sqrt{m}}_{1}l}{{\sqrt{m}}_1+\sqrt{m_2}}$

$x=\frac{\sqrt{m}r}{\sqrt{m}+\sqrt{4m}}=\frac{r}{3}$

Now potential at $P$ will be equal to sum of potentials due to $m$ and $4m$.
$V_P=-\frac{Gm}{r/3}+\left(\frac{-G\times 4m}{2r/3}\right)$
$\Rightarrow V_P=\frac{-9Gm}{r}$

Why this question? Note : The gravitational potential at a point is equal to the sum of gravitational potentials due to all masses in the vicinity. Also gravitational potential is a scalar quantity and hence algebraic sum is sufficient. Key Concept: The gravitational potential due to a point mass is given by $V=-\frac{Gm}{r}$