Question

The gravitational force acting on a particle of 1 g due to a similar particle is equal to $6.67\times {10}^{-17}N.$ Calculate the separation between the particles.

Answer 1

Given,

$m=1gm=\frac{1}{1000}kg$

$F=6.67\times {10}^{-17}N$

We know, $F=\frac{G{m}_1{m}_2}{r^2}$

$\therefore 6.67\times {10}^{-17}$

= $\frac{6.67\times {10}^{-11}\times \left(1/1000\right)\times \left(1/1000\right)}{r^2}$

$\Rightarrow r^2=\frac{6.67\times {10}^{-6}\times {10}^{-11}}{6.67\times {10}^{-17}}$

$=\frac{{10}^{-17}}{{10}^{-17}=1}$

$\Rightarrow r=\sqrt{1}=1$ metre

So, the separation between the particles is 1 m.