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

The correct option is A zero

The situation is as shown in the figure.
Let P is the midpoint of the line joining the centers 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 directions)

$=\frac{GMm}{{\left(5R\right)}^2}-\frac{GMm}{{\left(5R\right)}^2}=0$