Question

Two spheres of radius $r=0.5m$ and mass $m=1kg$ are placed in contact with each other, what will be the gravitational force between them:

• A. $0N$, since the spheres are touching each other and r=0
• B. $6.67\times {10}^{-11}N$
• C. $6.67\times {10}^{-4}N$
• D. $6.67\times {10}^{-6}N$

Answer 1

Answer: (B)

$6.67\times {10}^{-11}N$

The centre of mass of each sphere lies at the centre of the sphere. Thus, the spheres can be considered to be equal to point masses and they are separated by a distance equal to $R=2\times r=1m$

The gravitational force of attraction is given by $F=\frac{G{m}_1{m}_2}{R^2}$

Hence,
The force of attraction between them is $F=\frac{G{m}^2}{R^2}=\frac{G{1}^2}{1^2}=6.67\times {10}^{-11}N$
The correct option is (B)