A force of 200N acts between two objects at a certain distance apart. The value of the force when the distance is halved is
A. 400N B. 200N C. 100N D. 800N
Correct Answer: D
Explanation
let the masses of the two objects be M1 and M2 and their distance apart = r Therefore the force acting F1 = \( \frac{GM1M2}{r^2} \) for a new distance of r/2, we have a force of F2 = \( \frac{GM2M2}{r/2} \\ \text{Thus } F1 \times r^2 = GM1M1 \text{and} \\ F2 \times (r/2)^2 = GM1M1 \\ \text{Since } GM1M1 = GM1M1 \\ \implies F1 \times r^2 = F2 \times (r/2)^2 \\ \text{Therefore } 200 \times r^2 = F2 \times r^2/4 \\ F2 = \frac{4 \times 200 \times r^2}{r^2} = 800N \)