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: Option 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 )