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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.
Solution
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.
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