An irregularly shaped object that is 10 m long is placed with each end on a scale. If the scale on the right reads 96 N while the scale on the left reads 71 N, how far from the left end is the center of
Gravity of this object?
A) 4.3 m
B) 5.7 m
C) 7.4 m
D) 14 m

Question

Quizplus · Accepted Answer

The center of gravity can be found using the principle of moments. The total weight of the object is the sum of the readings of the two scales, which is 96 N + 71 N = 167 N. Let $x$ be the distance from the left end to the center of gravity. The moment about the left end is then $x \times 167 \, \text{N}$. This must equal the moment produced by the right scale about the left end, which is $10 \, \text{m} - x$ times the force on the right scale (96 N). Setting these equal gives $x \times 167 \, \text{N} = (10 - x) \times 96 \, \text{N}$. Solving for $x$ gives the position of the center of gravity from the left end. The correct calculation leads to $x = 5.7 \, \text{m}$, hence option B is correct.

An Irregularly Shaped Object That Is 10 M Long Is