Question

The object in figure is constructed of uniform wire bent into the shape from for the figure shown below the center of mass w.r.t. given frame is

• A. $(\frac{1}{2}\cos \frac{\theta }{2},\frac{1}{2}\sin \frac{\theta }{2})$
• B. $(\frac{1}{4}{\cos }^2\left(\frac{\theta }{2}\right)\cdot \frac{1}{8}\sin \theta )$
• C. $(\frac{1}{2}{\sin }^2\left(\frac{\theta }{2}\right),\frac{1}{2})$
• D. $(\frac{1}{2},\frac{1}{2}{\cos }^2\theta )$

Answer 1

The correct option is B $(\frac{1}{4}{\cos }^2\left(\frac{\theta }{2}\right)\cdot \frac{1}{8}\sin \theta )$

$\begin{array}{c}Ycom=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}\\ =\frac{m_1\left(0\right)+m\left(\frac{l}{u}\sin \theta \right)}{2m}\\ =\frac{l}{8}\sin \theta \\ Hence,theoptionBisthecorrectanswer.\end{array}$