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

### Question

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

### 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 = $$\frac{GM2M2}{r/2} \\ \text{Thus } F1 \times r^2 = GM1M1 \text{and} \\ F2 \times (r/2)^2 = GM1M1 \\ \text{Since } GM1M1 = GM1M1 \\ \implies F1 \times r^2 = F2 \times (r/2)^2 \\ \text{Therefore } 200 \times r^2 = F2 \times r^2/4 \\ F2 = \frac{4 \times 200 \times r^2}{r^2} = 800N$$

## Dicussion (1)

• 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 = $$\frac{GM2M2}{r/2} \\ \text{Thus } F1 \times r^2 = GM1M1 \text{and} \\ F2 \times (r/2)^2 = GM1M1 \\ \text{Since } GM1M1 = GM1M1 \\ \implies F1 \times r^2 = F2 \times (r/2)^2 \\ \text{Therefore } 200 \times r^2 = F2 \times r^2/4 \\ F2 = \frac{4 \times 200 \times r^2}{r^2} = 800N$$