Question

Three men A, B, C of mass 40kg,50kg and 60 kg are standing on a plank of mass 90kg which is kept on a smooth horizontal plane B sits in the middle of the plane B sits in the middle of the plane A and C sit 2 meters away from opposite sides. If A and C exchange there positions then mass B will shift

Answer 1

The center of mass (CM) cannot shift position. Therefore, the CM of the system must remain the same before and after the exchange.

The equation of the position of the CM is given by:

$x_{cm}=\frac{m_A{x}_A+m_B{x}_B+m_C{x}_C}{m_A+m_B+m_C+M}$

Before the exchange: $x_{cm1}=\frac{40(-2)+50\left(0\right)+60\left(2\right)}{40+50+60+90}=\frac{1}{6}m$

After the exchange: $x_{cm2}=\frac{60(-2)+50\left(0\right)+40\left(2\right)}{40+50+60+90}=\frac{-1}{6}m$

Therefore, mass B will shift by: $x_{cm1}-x_{cm2}=\frac{1}{3}m$ towards the right.