Question

Three man A, B and C of mass $40kg,50kg,60kg$ are standing on a plank of mass $90kg$, which is kept on a smooth horizontal plane. If A and C exchange their positions then mass B will shift:

• A. 1/3 m towards left
• B. 1/3m towards right
• C. will not move w.r.t ground
• D. 5/3m towards left

Answer 1

The correct option is B 1/3m towards right

The physics of this question is that the center of mass(CM) cannot move. All of the forces are internal forces so the CM of the system must remain in the same place. We can now write the position of the CM before the switch and the exchange and then set them equal. The CM of the center of the plank is

$x_{CM}=\frac{m_a{x}_a+m_b{x}_b+m_c{x}_c}{m_a+m_b+m_c+M}$

$x_{C{M}_1}=\frac{40\times (-2)+50\times 0+60\times 0}{40+50+60+90}=\frac{1}{6}m$

$x_{C{M}_2}=\frac{60\times (-2)+50\times 0+40\times 0}{40+50+60+90}=-\frac{1}{6}m$

Thus, the mass will shift $x_{C{M}_1}-x_{C{M}_2}=\frac{2}{6}=\frac{1}{3}$ towards right