Question

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

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

Answer 1

Answer: (A)

Zero

Answer 2

The situation is as shown in the figure.

Let P is the midpoint of the line joining the centres of the spheres.

The gravitational force on mass m due to sphere A is

The gravitational forces on mass m due to sphere B is

$\mathrm { F } _ { 2 } = \frac { \mathrm { GMm } } { ( 5 \mathrm { R } ) ^ { 2 } }$ along $\mathrm { PO } _ { 2 }$

Net force on mass m is

($\mathrm { F } _ { 1 }$and are opposite in directions)