Question

Three man $A,B\&C$ of mass $40kg,50kg\&60$ $kg$ 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. $1/3m$ 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

Centre of mass of whole system will remain unchanged before and after shifting exchanging of position of $A$ and $C$

Let change in position of man $B$ after exchanging is $x$ then change position of plank will be also $x$ ,change in Position of $A$ will be $x+4$ and change position of $C$ will be $x-4$

Now change in position of center of mass before exchange after exchange is $0$ therefore,

$△x_{cm}=\frac{m_A△x_A+m_B△x_B+m_c△x_c+m_p{△x}_p}{m_A+m_B+m_c+m_p}$

Substitute all value in above equation

$0=\frac{40\times (x+4)+50\times x+60(x-4)+90\times x}{40+50+60+90}40x+160+50x+60x-240+90x=0240x-80=0x=\frac{80}{240}x=\frac{1}{3}$

Hence, mass $B$ will shift $1/3m$ towards right.Correct option is $B$