Question

Two rods $PQ$ and $RS$ of identical mass and lengths $12\text{cm}$ and $18\text{cm}$ are joined to form a $T$ - shaped frame as shown in the figure. If the centre of mass of a rod is at the mid point of the rod, the location of centre of mass of the $T$ - shaped frame (w.r.t point $R$) is

• A. $(0,-9)\text{cm}$
• B. $(0,-4.5)\text{cm}$
• C. $(-4.5,0)\text{cm}$
• D. $(4.5,-4.5)\text{cm}$

Answer 1

The correct option is B $(0,-4.5)\text{cm}$


From figure, $R$ is considered as the origin of $x-y$ co-ordinate system
$\therefore$ COM of rod $PQ=(x_1,y_1)=(0,0)$
COM of rod $RS=(x_2,y_2)=(0,-9)$
Let ${}^{\prime }{C}^{\prime }$ be the centre of mass of $T$ shape frame
$C_x=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}=\frac{m\left(0\right)+m\left(0\right)}{2m}=0$
$C_y=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}=\frac{m\left(0\right)+m(-9)}{2m}=-4.5\text{cm}$
$\therefore$ location of COM $C=(0,-4.5)\text{cm}$