Question

Locate the centre of mass of arrangement shown in figure . The three rods are identical in mass and length

• A. $(\frac{1}{2},\frac{1}{2})$
• B. $(\frac{L}{3},0)$
• C. $(\frac{L}{3},\frac{L}{2})$
• D. $(0,\frac{2}{3})$

Answer 1

Answer: (A), (C)

The correct options are
A $(\frac{1}{2},\frac{1}{2})$
C $(\frac{L}{3},\frac{L}{2})$

Here, the coordinates of the centre of mass of the three rods are:

$(0,\frac{L}{2}),(\frac{L}{2},0),(\frac{L}{2},L)$

The arrangement is symmetric about the line $y=\frac{L}{2}$

Hence the $y$ coordinate of the centre of mass is $\frac{L}{2}$.

Now, $x$ coordinate of the centre of mass $=\frac{\sum m_i{x}_i}{\sum m_i}$

$=\frac{L}{3}$

Therefore, the centre of mass of the arrangement is at $(\frac{L}{3},\frac{L}{2})$