Question

Four bodies of masses 2,3,5 and 8 kg are placed at the four corners of a square of side 2 m. The position of CM will be

• A. $(\frac{8}{9},\frac{13}{9})$
• B. $(\frac{16}{18},\frac{26}{18})$
• C. $(\frac{11}{9},\frac{13}{9})$
• D. $(\frac{11}{9},\frac{8}{9})$

Answer 1

The correct option is A $(\frac{8}{9},\frac{13}{9})$

Suppose the mass $2kg$ is at $O$ $(0,0)$ and

the mass $3kg$ is at $A$ $(2,0)$ ,

the mass $5kg$ is at $B$ $(2,2)$

and the mass $8kg$ is at $C$ $(0,2)$

then the center of mass will be at $(x,y)$ , given by

$x=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3+m_4{x}_4}{m_1+m_2+m_3+m_4}=\frac{2\times 0+3\times 2+5\times 2+8\times 0}{2+3+5+8}=\frac{8}{9}$

similarly $y=\frac{13}{9}$