Answer:
16 times as strong
Explanation:
From the question given above, the following assumptions were made:
Initial Force (F₁) = F
Initial distance apart (r₁) = r
Final distance apart (r₂) = ¼r
Final force (F₂) =?
Next, we shall obtain a relationship between the force and the distance apart. This can be obtained as follow:
F = GM₁M₂ / r²
Cross multiply
Fr² = GM₁M₂
If G, M₁ and M₂ are kept constant, then,
F₁r₁² = F₂r₂²
Finally, we determine the new force as follow:
Initial Force (F₁) = F
Initial distance apart (r₁) = r
Final distance apart (r₂) = ¼r
Final force (F₂) =?
Fr² = F₂ × (¼r)²
Fr² = F₂ × r²/16
Fr² = F₂r² / 16
Cross multiply
16Fr² = F₂r²
Divide both side by r²
F₂ = 16Fr² / r²
F₂ = 16F
From the calculations made above, we can see that the new force is 16 times the original force.
Thus, the new force is 16 times stronger.
