Question

Four particles of masses \(m_1=1\) kg, \(m_2=2\) kg, \(m_3=1\) kg and \(m_4=m\) are placed at the four corners of a square. The mass \(m_4\) required, so that the centre of mass of all the four particles is exactly at the centre of the square is

• A. \(3\) kg
• B. \(4\) kg
• C. \(1.5\) kg
• D. \(0.5\) kg
• E. \(2\) kg

Hint:

For center of mass at the center of a square, masses must balance symmetrically about both axes.

Answer 1

Answer: (E)

For the centre of mass to be at the centre of the square, opposite corners must balance in both \(x\) and \(y\) directions. This requires: \[ m_1+m_4=m_2+m_3 \] \[ 1+m=2+1 \] \[ 1+m=3 \Rightarrow m=2 \] Hence, \[ \boxed{(E)\ 2\text{ kg}} \]