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 figure. Locate the centre of mass of the combination, assuming same mass per unit area for the two plates.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the mass per unit area (which is same for square and circular disc)$=\sigma$
Then mass of square plate = $d^2\sigma$ and mass of circular disc = $\frac{\sigma \pi d^2}{4}$ = $m_2$
Taking O as origin,We know, comof square plate will be at
$(\frac{d}{2},0)$ and COM of circular disc = $(\frac{3d}{2},0)$
COM of system = $\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$
= $\frac{d^2\sigma x\frac{d}{2}+\sigma \pi \frac{d^2}{4}\left(\frac{3d}{2}\right)}{\sigma (d^2+\frac{\pi d^2}{4})}$
= $\frac{\frac{d}{2}+\frac{3\pi }{r}d}{1+\frac{\pi }{4}}=\frac{2d+\frac{3\pi }{2}d}{4+\pi }$
= $\frac{(4+3\pi )d}{2(4+\pi )}$
$\therefore$ com of system is $\frac{(4+3\pi )d}{2(4+\pi )}$ units away from assumed origin, towards right.