Question

Determine the position of center of mass of the T shaped plate of negligible thickness as shown.

Answer 1

Refer fig.1

This is a T-shared homogeneous object. We need to find com of the object.

Let us divide this T-shared object into two piece and call masses as $m_1$ and $m_2$ of the two pieces.

Refer fig.2 and 3.

Since it is homogeneous we can consider mass $\alpha$ Area.

So, $m_1=6\times 2=12m^2$

$m_2=4\times 2=8m^2$

Choose ${}^{\prime }{O}^{\prime }$ as origin,

COM must lie on dotted line which is $3m$ away from origin along X-axis

$Y_{CM}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}=\frac{12\times 5+8\times 2}{12+8}=\frac{60+16}{20}=\frac{76}{20}=\frac{19}{6}=3.8m$

$\therefore COM=(X_{CM},Y_{CM})=(3m,3.8m)$