Question

The gravitational force between two objects is 49N.How much distance between these objects be decreased so that the force become doubled? ​

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

The gravitational force between two objects is 49N

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

How much distance b/w them be decreased so that force become doubled.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

✣ Gravitational force acts between two point masses is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

$\dag\:\boxed{\bf{\red{F\propto\:\dfrac{1}{r^2}}}}$

Let initial distance between two objects be r.

$:\implies\tt\:\dfrac{F}{F'}=\dfrac{{r'}^2}{r^2}$

ATQ, F' = 2F = 98

$:\implies\tt\:\dfrac{49}{98}=\dfrac{{r'}^2}{r^2}$

$:\implies\tt\:{r'}^2=\dfrac{r^2}{2}$

$:\implies\boxed{\bf{\purple{r'=\dfrac{r}{\sqrt{2}}}}}$