Question

How does the gravitational force of attraction between two objects having fixed mass vary if the distance between th is tripled

from:
chapter:force
topic:gravitation
class:10

i need quick answer​

Answer 1

The given question is  the gravitational force of attraction between two objects having fixed mass vary if the distance between them is tripled.

we have to find how it takes place.

It is found by using the formula

$F = ((G*m1*m2)/r^2)$

Where -G is the universal gravitational constant equal to$6.67 * 10^{-11}$

m1 is the mass of body one

m2 is the mass of body two

r is the distance between the two bodies

From the equation we realise that Force is inversely proportional to$r^2$(distance squared), so tripling the distance will cause the force is be a ninth ($(\frac{1}{9} )*F$

If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).

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Answer 2

Concept

For two particles of mass m₁ and m₂, the gravitational force between them is given by an empirical relation

     F = Gm₁m₂ / r²,         ...(1)

where r is the distance between the two particles,

G is a constant, called the Gravitational constant.

Given

• The distance between the two bodies is tripled.
• The masses of the two bodies are held fixed in changing the distance.

Find

How the force between the two masses varies.

Solution

Distances between the bodies

Let the initial distance between them be r₁, and the final distance be r₂. It is given that the final distance is three times the initial distance i.e.,

               r₂ = 3r₁ .                         ...(2)

Initial force between the masses

Using the relation (1) the initial force between the two bodies is

               F₁ = Gm₁m₂ / r₁².                   ...(3)

Final force between the bodies

Again using the relation (1) the final force between the two bodies is

                F₂ = Gm₁m₂ / r₂².                  ...(4)

Relation between the initial and final forces

Using the value of r₂ from equation (2) the above equation becomes

                F₂ = Gm₁m₂ / (3r₁)² = Gm₁m₂ / 9r₁².

Using the equation (3) in the above equation we get,

                F₂ = F₁ / 9.

The force between the two bodies is reduced by a factor of 9.

#SPJ2