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. Then the centre of mass of the combination will be (assume same mass per unit area for the two plates)

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

Answer 1

Answer: (C)

Taking centre of the disc as origin,
$x$ coordinate of the disc,
$x_{1}=0$
$x$ coordinate of Plate,
$x_{2}=\frac{d}{2}+\frac{d}{2}=d$

centre of mass of the combination,
$x_{c m}=\frac{A_{1} x_{1} + A_{2} x_{2}}{A_{1} + A_{2}}$
$x_{c m}=\frac{0 + \left(d^{2}\right) d}{\frac{\pi d^{2}}{4} + d^{2}}$
$x_{c m}=\frac{4 d}{4 + \pi }$