Question

The gravitational force produce between any two object kept 2.5×10 to the power 4 km apart is 580N.At what distance should they kept so that the grqvitation force becomes half.​

Answer 1

d = 3.54 x 10⁴ Km

Step-by-step explanation:

Given,

The distance between the two objects, r = 2.5 x 10⁴ Km

The gravitational force between them, F = 580 N

The gravitational force between the two objects is given by the formula

F = GMm/r² newton

When the gravitational force becomes half, then the distance between them becomes

Let us multiply the above equation by 1/2 on both sides

( 1/2) F = (1/2) GMm/r²

= GMm/2r²

= GMm/(√2r)²

Therefore, the distance becomes √2d, when the gravitational force between them becomes half

d = √2r = √2 x 2.5 x 10⁴ Km

= 3.54 x 10⁴ Km

Hence, the two objects should be kept at a distance, d = 3.54 x 10⁴ Km so that the gravitational force becomes half.