Question

The gravitational force between two objects is 45,000 N. What will be the gravitational force between the two objects if the distance between the objects is reduced by one-half? 11,250 N 22,500 N 90,000 N 180,000 N

Answer 1

The gravitational force would be 180,000 N if the distance is reduced by one- half.

According to Newton's law of gravitation, the force of attraction between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

Therefore, the force F between the two masses when they are at a distance d apart can be written as

$F \alpha\frac{1}{d^2}$   ........(1)

When the distance between the two objects is reduced to one- half, then the new force F₁ is given by,

$F_1\alpha\frac{1}{(\frac{d}{2})^2} \\ F_1\alpha\frac{4}{d^2} ......(2)$

Divide equation (2) by equation (1)

$\frac{F_1}{F} =4\\ F_1 =4F$

Substitute 45,000 N for F.

$F_1 =(4)(45,000 N)\\ = 180,000 N$

If the distance between the two objects is reduced by one- half, the force between them has a value 180,000 N.