Question

if the first mass increases 3 times, second mass increases 5 times and the distance increases 2 times, how does the force of gravitation change?

Answer 1

According to Newton 's law of Gravitation :
Gravitational Force ( say F ) is given by :
F = Gmm'/r²
where ,
G is the universal Gravitational constant .
m and m' are the masses of the two bodies .
r is the distance between them .

Now according to question:
m→ 3m
m' → 5m'
r → 2r
then the New Gravitational force ( say F') between them is given by :
F ' = G(3m)(5m')/(2r)²
=> F' = (15/4) ×( Gmm'/r²)
=> F' = 15/4 F
=> New Gravitational force between them is increased by 15/4 times then the initial .
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hope it helps!

Answer 2

let two bodies which masses are m and M seperate r distance ,

Then F = GMm/r²

now ,
m" = 3m
M" = 5M
r" =2r

F" = Gm"M"/r"²
=G(3m)(5M)/(2r)² =(15/4)GmM/r²

from above ,
F" = 15F/4
change in Force = 15F/4 - F = 11F/4

% change = 1100/4 = 275 ℅