Question

The gravitational force acting on a particle of 1 g due to a similar particle is equal to 6.67 × 10⁻¹⁷ N. Calculate the separation between the particles.

Answer 1

Mass of the particle, m = 1 gm$=\frac{1}{1000}\mathrm{kg}$
Let the distance between the two particles be r.
Gravitational force between the particle, F = 6.67 × 10⁻¹⁷ N
Also, $\mathrm{F}=\frac{G{m}_1{m}_2}{r^2}$
Substituting the respective values in the above formula, we get:
$$\begin{gathered} 6.67\times {10}^{-17}=\frac{6.67\times {10}^{-11}\times \left(1/1000\right)\times \left(1/1000\right)}{r^2} \\ \Rightarrow r^2=\frac{6.67\times {10}^{-6}\times {10}^{-11}}{6.67\times {10}^{-17}} \\ =\frac{{10}^{-17}}{{10}^{-17}}=1 \\ \Rightarrow r=\sqrt{1}=1\mathrm{m} \end{gathered}$$
∴ The separation between the particles is 1 m.