Question

Figure shows a composite system of two uniform rods of length as shown. The co-ordinates of the centre of mass of the system of rods are

• A. \(\left(\frac{L}{2},\frac{2L}{3}\right)\)
• B. \(\left(\frac{L}{4},\frac{2L}{3}\right)\)
• C. \(\left(\frac{L}{6},\frac{2L}{3}\right)\)
• D. \(\left(\frac{L}{6},\frac{L}{3}\right)\)

Hint:

Treat each rod as a point mass at its own centre and take the mass-weighted average of the coordinates.

Answer 1

The Correct Option is C

Step 1: Mass Ratio
The vertical rod is twice as long, so its mass is twice that of the horizontal rod. Let the masses be $m$ and $2m$.

Step 2: Substitution
$x_{cm}=\dfrac{m(L/2)}{3m}=\dfrac{L}{6}$ and $y_{cm}=\dfrac{2m(L)}{3m}=\dfrac{2L}{3}$.

Step 3: Compare the options
Only option (C) has $\left(\dfrac{L}{6},\dfrac{2L}{3}\right)$.

Final Answer:
The centre of mass coordinates are (L/6, 2L/3). \[ \boxed{\text{(C) }\left(\dfrac{L}{6},\dfrac{2L}{3}\right)} \]