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 \[= \frac{1}{1000} kg\]

Let the distance between the two particles be r.
Gravitational force between the particle, F = 6.67 × 10⁻¹⁷ N

Also, \[F = \frac{\text{ G m} _1 \text{ m }_2}{r^2}\]

Substituting the respective values in the above formula, we get :

\[6 . 67 \times {10}^{- 17} = \frac{6 . 67 \times {10}^{- 11} \times \left( 1/1000 \right) \times \left( 1/1000 \right)}{r^2}\]

\[ \Rightarrow r^2 = \frac{6 . 67 \times {10}^{- 6} \times {10}^{- 11}}{6 . 67 \times {10}^{- 17}}\]

\[ = \frac{{10}^{- 17}}{{10}^{- 17}} = 1\]

\[ \Rightarrow r = \sqrt{1} = 1 \text{ m }\]

∴ The separation between the particles is 1 m.