Question

The gravitational force of attraction between two objects is x. Keeping the masses of the objects unchanged, if the distance between the objects is halved, then the magnitude of gravitational force between them will become :

(a) $x/4$
(b) $x/2$
(c) $2x$
(d) $4x$

Answer 1

Option (d) is correct.

According to the Universal law of gravitation,

$F=G\frac{Mm}{r^2}$

Since the masses of the objects remains the same, we have'

$F\propto \frac{1}{r^2}$

Given,

$r_1=r$, $r_2=\frac{r}{2}$ and $F_1=x$

$\frac{F_2}{F_1}=\frac{{r_1}^2}{{r_2}^2}=4$

$F_2=4x$.