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

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) (2GMm/25R2) (C) (GMm/25R2) (D) (GMm/100R2)

Tardigrade Admin · Accepted Answer

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{GM m}{( 5 R ) ^{2}}

along

P O_{1}

The gravitational force on mass

m

due to sphere

B

is

F_{2} = \frac{GM m}{( 5 R ) ^{2}}

along

P O_{2}

Net force on mass

m

is

F_{R} = F_{1} - F_{2}

(

∵ F_{1}

and

F_{2}

are opposite in direction)

= \frac{GM m}{( 5 R ) ^{2}} - \frac{GM m}{( 5 R ) ^{2}} = 0

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

zero

$\frac{2 GM m}{25 R ^{2}}$

$\frac{GM m}{25 R ^{2}}$

$\frac{GM m}{100 R ^{2}}$

Q. 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

zero

25R22GMm​

25R2GMm​

100R2GMm​

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

$\frac{2 GM m}{25 R ^{2}}$

$\frac{GM m}{25 R ^{2}}$

$\frac{GM m}{100 R ^{2}}$