A uniform piece of wire,20 cm long,is bent in a right angle in the center to give it an L-shape.How far from the bend is the center of mass of the bent wire?
A) 2.5 cm
B) 3.5 cm
C) 4.5 cm
D) 5.0 cm
E) 7.1 cm

Question

Quizplus · Accepted Answer

The center of mass of each segment of the wire (10 cm long) is at its midpoint, 5 cm from the bend. Since the wire is uniform and the segments are equal in length, the center of mass of the L-shape will be located at the point where the medians of the right triangle (formed by the two segments and the line connecting their midpoints) intersect. This point is 1/3 of the way along the median from the right angle, which is $\sqrt{5^2 + 5^2} = \sqrt{50}$ cm long. Therefore, the distance from the bend to the center of mass is $\frac{1}{3} \times \sqrt{50} \approx 3.5$ cm.

A Uniform Piece of Wire,20 Cm Long,is Bent in a Right