A wooden plank of mass `20kg` is resting on a smooth horizontal floor. A man of mass `60kg` starts moving from one end of the plank to the other end. The length of the plank is `10m`. Find the displacement of the plank over the floor when the man reaches the other end of the plank.

Explanation

Here the system is man + plank. Net force on this system in horizontal direction is zero and initially the center of mass of the system is at rest. Therefore, the center of mass does not move in horizontal direction.
Let x be the displacement of the plank. Assuming the origin i.e., x=0 at the position shown in figure.

As we said earlier also, the center of the mass will not mover in horizontal direction (X-axis). Therefore, for center of mass to remain stationary,
`x_(i) = x_(f)`
`(60(0) + 20(10/2))/(60 + 20) = (60(10-x) + 20(10/2-x))/(60 + 20)`
or `5/4 = (6(10-x) + 2(10/2-x))/8=(60-6x+10-2x)/(8)`
` or 5=30-3x +5-x or 4x = 30 or x=30/4 m or x=7.5m`
Note The center of mass of the plank lies at its center.