Question

Three rods of same mass are placed as shown in figure. The co-ordinates of centre of mass of the system are

• A. \((\frac{\mathrm{a}}{3},\frac{\mathrm{a}}{3})\)
• B. \((a,\frac{a}{2})\)
• C. \((2a,\frac{a}{2})\)
• D. \((\frac{2a}{3},\frac{a}{3})\)

Hint:

Each rod has the same mass, so treat each as a point mass at its own midpoint and average the coordinates.

Answer 1

The Correct Option is D

Step 1: Formula
$x_{cm}=\frac{\sum m_ix_i}{\sum m_i}$ and similarly for $y$, with equal masses $m$.

Step 2: Substitute
$x_{cm}=\frac{m(0)+m(a)+m(a)}{3m}=\frac{2a}{3}$, $y_{cm}=\frac{m\frac{a}{2}+m(0)+m\frac{a}{2}}{3m}=\frac{a}{3}$.

Step 3: Result
The coordinates $\left(\frac{2a}{3},\frac{a}{3}\right)$ match option (D).

Final Answer:
Option (D) is correct. \[ \boxed{\text{(D) }\left(\dfrac{2a}{3},\dfrac{a}{3}\right)} \]