What happens to the gravitational force when distance is doubled
The Relationship Between Gravitational Force, Masses and Distance Between Two Points:
1) What happens to the gravitational force when distance is doubled keeping the masses constant?
Here,
We know that, F = GMm/d^2 -------------------(1)
When distance is doubled keeping the mass constant
F' = GMm/〖(2d)〗^2 = GMm/〖4d〗^2 = F/4 (∵ From eqn(i)]
So, the gravitational force decreases by 4 times.
2)What will happens to the gravitational force when the distance is decreased to half keeping the masses constant?
Here ,
We know that, F = GMm/d^2 -----------------------(1)
When the distance is decreased to half keeping the masses constant.
Then,
F' = GMm/〖(d/2)〗^2 = GMm/(d^2/4) = 4GMm/d^2 = 4F [since from eqn(1)]
3) What will happens to the gravitational force when the mass of both bodies is decreased to half?
Here,
When the mass of both bodies is decreased to half , then,
F' = (G(M/2)(m/2))/d^2 = GMm/(4d^2 ) = F/4 [∵ From eqn(i)]
4) What will happen to the gravitational force of attraction between two bodies when the mass of each body is doubled and the distance between them is tripled?
Here,
Gravitational force of attraction between two bodies is given by,
F = GMm/d^2 -----------------------(1)
When the mass of each body is doubled then the new masses will be M = 2M , m = 2m and if the distance is tripled , then d = 3d,
So,
F' = (G(2M)(2m))/〖(3d)〗^2
F' = 4GMm/〖9d〗^2
After putting the value of F from the equation (i), we have
∴ F' = 4/9 F
∴ The magnitude of the force reduces to 4/9 of the initial force.
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