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

Question

Quizplus · Accepted Answer

The center of gravity of an irregularly shaped object is the point where the weight of the object can be considered to act. To find the center of gravity, we need to use the principle of moments.

Let's assume that the distance from the left end of the object to the center of gravity is x. The distance from the center of gravity to the right end of the object is (10 - x). The weight of the object acts downward, so we can consider the clockwise moments as negative and the counterclockwise moments as positive.

The moment of the weight with respect to the left end of the object is:

-71N * 10m = -710 Nm

The moment of the weight with respect to the center of gravity is:

96N * (10 - x)m = 960 Nm - 96Nx

Since the object is in equilibrium, the sum of the moments about any point must be zero. So we can set the two moments equal to each other and solve for x:

-710 Nm = 960 Nm - 96Nx

2660 Nm = 96Nx

x = 27.7/9 m = 3.08 m

Therefore, the distance from the left end of the object to the center of gravity is 3.08 m. Since we want the distance from the center of gravity to the left end, we can subtract this from the total length of the object:

10 m - 3.08 m = 6.92 m

So the center of gravity is approximately 6.92 m from the left end of the object, or 10 - 6.92 = 3.08 m from the right end of the object.

The closest answer choice is A) 5.7 m, which is the same as 10 - 4.3 m. This is not the correct answer, but it is close. Therefore, we can eliminate all other answer choices and choose A) 5.7 m as the best choice.

An Irregularly Shaped Object That Is 10 M Long Is 96 N96 \mathrm {~N}96 N

An Irregularly Shaped Object That Is 10 M Long Is $96 \mathrm {~N}$