Two small objects, with masses m and m, are originally a distance r apart, and the gravitational force on each one has magnitude f. the second object has its mass changes to 2m, and the distance is changed to r/4. what is the magnitude of the new gravitational force

32F

Explanation:

1) Formula

Universal Gravitaional Force, F = G M₁ M₂ / d²

2) Data:

M₁ = m
M₂ = m
d₁ = r

F₁ = F
M₂ = 2m

d = (r/4)
F₂ = ?

3) Solution:

i) Original force

F₁ = G (m)(m) / r² = G m² / r² = F

ii) Modified force

F₂ = G (m)(2m) / (r/4)² = G 2m² / (r² / 16) = 32 [Gm² / r²] = 32 F