If the distance between two objects is decreased to one fourth of the original distance how will the decrease change the force of attraction between the objects

F = GMm/r²

The relationship between F and r is an inverse one. So if the distance r decreases, to 1/4 the original distance:

Let F α 1/r²

F = k/r²

or F₂ / F₁ = (r₁ / r₂) ²

If r is decreased to 1/4,

F₂ / F₁ = (r₁ / r₂) ²

F₂ / F₁ = (r₁ / (1/4r₁)) ²

F₂ / F₁ = (4) ²

F₂ / F₁ = 16

F₂ = 16F ₁

The new force of attraction would be 16 times the former value.