A man of mass 80 kg stands on a plank of mass 40 kg. The plank is lying on a smooth horizontal floor. Initially both are at rest. The man starts walking on the plank towards north and stops after moving a distance of 6 m on the plank. Then (A) the centre of mass of plank-man system remains stationary. (B) the plank will slide to the north by a distance of 4 m (C) the plank will slide to the south by a distance of 4 m (D) the plank will slide to the south by a distance of 12 m

A man of mass $80 k g$ stands on a plank of mass $40 k g$ . The plank is lying on a smooth horizontal floor. Initially both are at rest. The man starts walking on the plank towards north and stops after moving a distance of $6 m$ on the plank. Then
(A) the centre of mass of plank-man system remains stationary.
(B) the plank will slide to the north by a distance of $4 m$
(C) the plank will slide to the south by a distance of $4 m$
(D) the plank will slide to the south by a distance of $12 m$

A
$A a n d B$
B
$A a n d C$
C
$o n l y D$
D
A and D

Solution:

Since net force is zero so centre of mass remains stationary

Let $x$ be the displacement of the plank.

Since $C M$ of the system remains stationary

so $80 (6 - x) = 40 x$

$\Rightarrow 12 - 2 x = x \Rightarrow x = 4 m .$

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