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

Options

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

Answer

B

Explanation

Let `x_(p) = x` sift of plank to the right
`Deltabar(x) = (m_(A) Deltax_(A) + m_(B) Deltax_(B) + m_(C ) Deltac_(c ) + m_(p)Deltax_(P))/(m_(A) + m_(B) + m_(C ) + m_(P))`
`0 = (40(x +4) + 50x + 60(x - 4) + 90x)/(40 + 50 + 60 + 90) rArr (1)/(3)m`