The gravitational force of attraction between two objects decreases by 36% when the distance between them is increased by 4 m. Find the original distance between them.

Explanation

Let force between the objects =F
Distance between them =r.
For case II distance, `r_1=(r+4)`
New force, `F_1=36%`, less than F
`:. F_1=F(1-(36)/(100))=(64)/(100)F`
`implies(G.m.m)/((r+4)^2)=(64)/(100)(G.m.m)/(r^2)`
`implies 100 r^2=64(r+4)^2` Take square roots on both sides.
` 10r=8(r+4) implies 10r=8r+32`
`implies (10-8)r=2r=32`
`r= 16 cm`.