A force of 200N acts between two objects at a certain distance apart. The value…

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 \)