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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

Options

A) 400N

B) 200N

C) 100N

D) 800N


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


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