Question

Two identical spheres each of mass $M$ and radius $R$ are separated by a distance $10R$. The gravitational force on mass $m$ placed at the midpoint of the line joining the centres of the spheres is

• A. zero
• B. $\frac{2GMm}{25R^{2}}$
• C. $\frac{GMm}{25R^{2}}$
• D. $\frac{GMm}{100R^{2}}$

Answer 1

Answer: (A)

The situation is as shown in the figure.

Let $P$ be the midpoint of the line joining the centres of the spheres.
The gravitational force on mass $m$ due to sphere $A$ is
$F_{1} = \frac{GMm}{\left(5R\right)^{2}}$ along $PO_{1}$
The gravitational force on mass $m$ due to sphere $B$ is
$F_{2} = \frac{GMm}{\left(5R\right)^{2} }$ along $PO_{2}$
Net force on mass $m$ is
$F_{R} = F_{1} - F_{2}$ ($\because F_{1}$ and $F_{2}$ are opposite in direction)
$= \frac{GMm}{\left(5R\right)^{2}} - \frac{GMm}{\left(5R\right)^{2} } = 0$