Question

Find the centre of mass of uniform L-shaped lamina (a thin flat plate) with dimensions as shown in figure. The mass of lamina is 3 kg

• A. $(\frac{5}{6}m,\frac{5}{6}m)$
• B. $(\frac{6}{5}m,\frac{6}{6}m)$
• C. $(\frac{5}{2}m,\frac{5}{6}m)$
• D. $(\frac{5}{3}m,\frac{6}{5}m)$

Answer 1

The correct option is A

$(\frac{5}{6}m,\frac{5}{6}m)$

The plate is uniform density and same thickness everywhere. So its C.M. will coincide with the centroid.

Divide the given plate into two parts of area $A_1$ and $A_2$ as shown in figure. We have
$A_1=2\times 1=2m^2$ with its centroid
$C_1(1,\frac{1}{2})$ and
$A_1=1\times 1=1m^2$ with its centroid $C_2(\frac{1}{2},\frac{3}{2})$
The centroid of whole plate can be defined as;
$\overline{x}=\frac{A_1{x}_1+A_2{x}_2}{A_1+A_2}=\frac{2\times 1+1\times \frac{1}{2}}{2+1}=\frac{5}{6}m$ and $\overline{y}=\frac{A_1{y}_1+A_2{y}_2}{A_1+A_2}=\frac{2\times \frac{1}{2}+1\times \frac{3}{2}}{2+1}=\frac{5}{6}m$