Question

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

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

Answer 1

The correct option is B 1/3 m towards right

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 exchange

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

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

After exchange

$x_{c{m}_2}\Rightarrow \frac{60(-2)+50\left(0\right)+40\left(2\right)}{40+50+60+90}$

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

Therefore mass (B) shift by

$x_{c{m}_1}-x_{c{m}_3}=\frac{1}{3}m$ towards.