Question

Four bodies of masses 2, 3, 5 and 8 kg are placed at the four corners of a square of side 2m in an anti-clockwise order with the 2kg mass at the origin. The position of the CM of the system will be

• A. $(\frac{8}{9},\frac{13}{9})$
• B. $(\frac{7}{9},\frac{11}{9})$
• C. $(\frac{11}{9},\frac{13}{9})$
• D. $(\frac{11}{9},\frac{8}{9})$

Answer 1

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

The co – coordinates of the corners of the square are (0, 0), (2, 0), (2, 2), (0, 2)
Hence, $X_{CM}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3+m_4{x}_4}{m_1+m_2+m_3+m_4}$
$=\frac{2\times 0+3\times 2+5\times 2+8\times 0}{2+3+5+8}=\frac{16}{18}=\frac{8}{9}m$
$Y_{CM}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3+m_4{y}_4}{m_1+m_2+m_3+m_4}$
$=\frac{2\times 0+3\times 0+5\times 2+8\times 2}{2+3+5+8}=\frac{26}{18}=\frac{13}{9}m$
$\therefore$ Coordinates of the centre of mass= $(\frac{8}{9},\frac{13}{9})$