Question

A force of 5.25 newtons acts on an object of unknown mass at a distance of 6.9 × 108 meters from the center of Earth. To increase the force to 2.5 times its original value, how far should the object be from the center of Earth?

Answer 1

4.36 x 10^8 m

Step-by-step explanation:

Let the mass of earth is M and unknown mass is m.

According to the Newton's law of gravitation, force between two objects is given by

`F = G(M m)/(d^(2))`

Here, F = 5.25 N, d = 6.9 x 10^8 m

`5.25 = G(M m)/((6.9* 10^(8))^(2))` .... (1)

Now, F' = 2.5 F and d be the distance

`2.5* 5.25 = G(M m)/((d)^(2))` ..... (2)

Divide equation (1) by equation by (2)

`(1)/(2.5) = \left ( (d)/(6.9* 10^(8)) \right )^(2)`

d = 4.36 x 10^8 m

Answer 2

The force between two objects is calculated through the equation,
F = Gm₁m₂/d²
where m₁ and m₂ are the masses of the objects. In this case, an unknown mass and Earth. d is the distance between them and G is universal gravitation constant.

In the second case, if the force is to become 2.5 times the original and all the variables are constant except d then,
2.5F = Gm₁m₂ / (D²)
D = 0.623d

Subsituting the known value of d,
D = 0.623(6.9 x 10^8) = 4.298 x 10^8 m