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Question
What happens to the gravitational force between two objects when the distance between them is :
(1) doubled ?
(2) halved ?
Solution
`F = (GMm)/r^2`
where,
F − gravitational force
G − gravitational constant
M − mass of the earth
m − mass of object
r − distance
(i). r = doubled
`F = (GMm)/r^2` keeping everything constant i.e. G, M, m
= `(GMm)/(2r)^2`
= `(GMm)/(4r^2)`
F becomes one-fourth.
(ii) r = halved
`F = (GMm)/r^2` keeping everything constant i.e. G, M, m
= `(GMm)/(1/(2r))^2`
= `(GMm)/(1/(4r))^2`
= `(4GM m)/(r^2)`
F becomes four times the original.
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