If the distance between two masses is increased by a factor of 5, by what factor would the m ass of one of them have to be altered to maintain the same gravitational force? Would there be an increase or decrease in the mass?
Gravitation force is given by:
F = G * M * m/ d2
Distance between the two masses is increased. So the new distance is D = 5d
New gravitational force, F1 = F
Let one of the masses is changed to m1 so as maintain the same gravitational force.
F1 = G * m1 * M/ D2
D = 5d
F = F1
G * m * M/ d2 = G * m1 * M/ D2
G * m * M/ d2 = G * m1 * M/ 25d2
= 25
m1 = 25m
Hence one of the masses should be increased by 25 times in order to have the same gravitational force.
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