Question

Five uniform rings, each of diameter $5\text{cm}$ and mass $10\text{g}$ are arranged as shown in the figure. Using the origin shown, the $y-$ co-ordinate of $COM$ of the five ring system is

• A. $4\text{cm}$
• B. $5\text{cm}$
• C. $0.4\text{cm}$
• D. $0.4\text{m}$

Answer 1

The correct option is A $4\text{cm}$

Centre of mass of each ring lies at the centre of ring.
Let $A,B,C,D$ and $E$ be the five uniform rings.
COM of ring $A(x_1,y_1)=(0,0)$
COM of ring $B(x_2,y_2)=(5,0)$
COM of ring $C(x_3,y_3)=(5,5)$
COM of ring $D(x_4,y_4)=(0,5)$
COM of ring $E(x_5,y_5)=(0,10)$


Let $y_{cm}$ be the $y-$ co-ordinate of COM of the five ring system.
$y_{cm}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3+m_4{y}_4+m_5{y}_5}{m_1+m_2+m_3+m_4+m_5}$
$=\frac{10(0+0+5+5+10)}{50}$
$=\frac{20}{5}=4\text{cm}$