Discussion
The force between two identical solid spheres each of radius r kept in contact is F . If the distance of their centres is made 4r, then the force between them is
Answer: B
The force becomes \(\frac{F}{4}\).
Uniform spheres attract as if their masses were at their centres. In contact, the centres are 2r apart; the new separation is 4r, twice as far. Gravitational force varies as the inverse square of the distance:
\[ F' = F\left(\frac{2r}{4r}\right)^{2} = \frac{F}{4} \]
The trap is to take the original distance as r (the radius) instead of 2r, which gives \(\frac{F}{16}\). \(\frac{F}{2}\) forgets to square the ratio.
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