Question

Two identical thin uniform rods of length $L$, each are joined to form T-shape as shown in the figure. The distance of centre of mass from $D$ is:

• A. $0$
• B. $L/4$
• C. $3L/4$
• D. $L$

Answer 1

The correct option is B $L/4$

Centre of mass of upper rod is at O.

Centre of mass of lower rod is at $\frac{L}{2}$ from O.

Along vertical line

$y_{cm}=\frac{(m1y1+m2y2)}{(m1+m2)}$

$=\frac{(0+\frac{mL}{2})}{\left(2m\right)}$

$=\frac{L}{4}$

∴ Centre of mass of system is at lower rod and below $\frac{L}{4}$ from point O