The gravitational force between two objects is 100 N. How should the distance between the objects be changed so that the force between them becomes 50 N.

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Solution

Given:
The gravitational force between two objects = 100 N.
Required to find:
The distance between the objects when the force between them becomes 50 N.
Solution:
Let the masses of the two objects be m₁ and m₂. The gravitational constant is G and the distance between the two objects is ‘R’.
The value of the gravitational force between two objects is given by $F = \frac{G m_{1} m_{2}}{R^{2}}$ .
From given,
$\frac{G m_{1} m_{2}}{R^{2}} = 100 N B y d i v i d i n g w i t h 2 o n b o t h s i d e s, w e g e t \Rightarrow \frac{G m_{1} m_{2}}{2 R^{2}} = 50 N B y c o n v e r t i n g i n t o t h e g e n e r a l e q u a t i o n o f t h e f o r c e o f g r a v i t a t i o n, w e g e t \Rightarrow \frac{G m_{1} m_{2}}{{(\sqrt{2} R)}^{2}} = 50 N$
Hence, the distance between the two bodies should become $\sqrt{2}$ times the original value.

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