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

Answer:

4.36 x 10^8 m

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

$F = G\frac{M m}{d^{2}}$

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

$5.25 = G\frac{M m}{(6.9\times 10^{8})^{2}}$       .... (1)

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

$2.5\times 5.25 = G\frac{M m}{(d)^{2}}$            ..... (2)

Divide equation (1) by equation by (2)

$\frac{1}{2.5} = \left ( \frac{d}{6.9\times 10^{8}} \right )^{2}$

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