Answer to Question #187658 in Mechanics | Relativity for Thasfin Ahmed

Question

A planar figure is formed from uniform wire that consists of two equal semi-circular arcs, each with its own closing diameter, joined so as to form a letter 'B' The figure is freely suspended from its top left hand corner.what angle does the straight edge of the figure make with the vertical?

Answer 1

Explanations & Calculations

• When suspended from a point always the centroid aligns with the vertical line as shown in the figure.
• This is true for any object suspended from a single point.
• The centroid of a semi-circle is located

$\qquad\qquad \begin{aligned} \small \bar{x}&=\small \frac{4a}{3\pi} \end{aligned}$ from the center.

• Therefore, the angle the figure makes when suspended vertically is

$\qquad\qquad \begin{aligned} \small \tan \theta &=\small \frac{\bar{x}}{2a}\\ &=\small \frac{2}{3\pi}\\ \small \theta &=\small \bold{11.981^0} \end{aligned}$

• By symmetry, it can be seen that the centroid of the entire figure is located inline with the joint. .