Question

Three men $A,B$ and $C$ of masses $40kg,50kg$ and $60kg$ 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. $1/3m$ 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 centre of mass cannot move at all. All the forces are internal forces so, the centre of mass will remain at the same place.

The centre of mass from the planck will be

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

Position of centre of mass before exchange :

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

$=\frac{1}{6}m$

Position of centre of mass after exchange :

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

$=\frac{-1}{6}m$

$x_{c{m}_1}-x_{c{m}_2}=\frac{1}{6}-\left(\frac{1}{6}\right)$

$=\frac{2}{6}$

$=\frac{1}{3}m$

So, the centre of mass will shift 1/3m towards right.