Question

A square plate of edge d and a circular disc of diameter d are placed touching each other at the midpoint of an edge of the plate as shown in the figure. The center of mass of the combination assuming same mass per unit area for two plates from the center of the disk is

• A. $\frac{2d}{2+\pi }$ left to the centra of disc
• B. $\frac{2d}{2+\pi }$ right to the centra of disc
• C. $\frac{4d}{4+\pi }$ right to the centra of disc
• D. $\frac{4d}{4+\pi }$ left to the centra of disc

Answer 1

The correct option is C $\frac{4d}{4+\pi }$ right to the centra of disc

Taking the center of disc as the $origin$ and the line joining its center with the center of the square as the $-$ x axis

we will get the coordinates of the center of mass of the disc as $(0,0)$

and that of the square plate as $(-(\frac{d}{2}+\frac{d}{2}),0)$ or $(-d,0)$

mass of the disc as $m_d=a\pi \frac{d^2}{4}$ where $a$ is mass density per unit area.

similarly mass of the square plate will be $m_s=a\times d^2$

so the center of mass will be at $x=\frac{m_d\times 0+m_s\times (-d)}{m_d+m_s}=-\frac{4d}{\pi +4}$ $negative$ so towards $left.$