two equal masses are separated by a certain distance and the force between them is 8 Newtons when the distance of separation is increased by 1 metre the force between them reduced to 2 Newtons find the initial distance of separation and their masses
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Explanation:
gravitational force in condition 1 = GmM =8N
r2
gravitational force in condition 2
=GmM =2N
R2
ratio of those 2 forces
= GmM * R2 =8/2
r2. GmM
=R2/r2 =4
=(R/r)2 =4
=R/r =2. [we know that R=r+1]
=(r+1)/r =2
=r+1=2r
=2r-r=1
=r=1m
hence, initial distance of separation is 1m
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