Question

If mass is uniformly distributed, find the distance $\left(\text{in m}\right)$ of the centre of mass of the T-shaped plate from point $O$.

• A. $\frac{19}{7}$
• B. $\frac{9}{7}$
• C. $\frac{7}{9}$
• D. $\frac{7}{19}$

Answer 1

The correct option is A $\frac{19}{7}$


Let T shape is made up of plate $A$ and $B$ and C.O.M of plates are $x_A$ and $x_B$ respectively.

Let mass density be $\sigma {\text{kg/m}}^2$
Mass of plate $A,m_A=l\times b\times \sigma =2\times 8\times \sigma \text{kg}=16\sigma \text{kg}$
Mass of plate $B,m_B=l\times b\times \sigma =6\times 2\times \sigma \text{kg}=12\sigma \text{kg}$
Choosing $O$ as origin
$X_{c.o.m}=\frac{m_A{x}_A+m_B{x}_B}{m_A+m_B}$
$=\frac{16\sigma \times 1+12\sigma \times 5}{16\sigma +12\sigma }=\frac{19}{7}$