Question

The distance of the centre of mass of the T - shaped plate from O is nearly equal to

• A. $7\text{m}$
• B. $2.7\text{m}$
• C. $4\text{m}$
• D. $1\text{m}$

Answer 1

The correct option is B $2.7\text{m}$


Taking parts A and B as two bodies of same system,
$m_1=l\times b\times \sigma =8\times 2\times \sigma =16\sigma$
$m_2=l\times b\times \sigma =6\times 2\times \sigma =12\sigma$
Choosing O as the origin and x axis along the vertical line of the figure
$x_1=1\text{m},x_2=2+3=5\text{m}$
$\therefore X_{CM}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$
$=\frac{16\sigma \times 1+12\sigma \times 5}{16\sigma +12\sigma }=\frac{19}{7}\text{m}=2.714\text{m}$


Hence, the correct anser is option (b).