How does the force of gravity between two bodies change
when the distance between them is tripled?
Answers
Answer:
The strength of the gravitational force between two objects depends on two factors, mass and distance. the force of gravity the masses exert on each other. If one of the masses is doubled, the force of gravity between the objects is doubled. increases, the force of gravity decreases.
Gravitational force F=
r
2
Gm
1
m
2
Case (i) : Mass of one object is doubled i.e m
1
′
=2m
1
∴ F
′
=
r
2
G(2m
1
)m
2
⟹F
′
=2F
Thus gravitational force gets also doubled
Case (ii) : Distance between the objects is doubled i.e r
′
=2r
∴ F
′
=
(2r)
2
Gm
1
m
2
⟹F
′
=
4
F
Thus gravitational force gets reduced by 4 times.
Distance between the objects is tripled i.e r
′
=3r
∴ F
′
=
(3r)
2
Gm
1
m
2
⟹F
′
=
9
F
Thus gravitational force gets reduced by 9 times.
Case (iii) : Mass of both the objects are doubled i.e m
1
′
=2m
1
and m
2
′
=2m
2
∴ F
′
=
r
2
G(2m
1
)(2m
2
)
⟹F
′
=4F
Thus gravitational force becomes 4 times.
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