Question

Man of 50 kg stands at one end of a plank of mass 200 kg and length 10 there is no friction between plant and ground while the there is friction between plank and man. find displacement of plank when man goes to other end

Answer 1

The Displacement of the plank is 6 m is the man goes to the other end.

Explanation:

Mass of the man m = 50 kg

Mass of the plank M = 200 kg

Length of the plank L = 10 m

When the man moves on the plank the plank will move in the direction opposite to the direction of motion of the man

Since there is no external force on the system (man + plank), the displacement of the centre of mass will be zero

Thus,

Let the displacement of the plank w.r.t. ground is x

Displacement of the man w.r.t. plank will be -L  (since displacement is in opposite direction)

Thus, displacement of the man w.r.t. Earth

= Displacement of the man w.r.t. plank + displacement of the plank w.r.t. earth

= x-L

The total movement of the centre of mass will be zero

Thus,

$m(x-L)-M(L/2-x) = 0$

or, $(m+M)x=\frac{ML}{2}+mL$

or, $x = \frac{ML/2+mL}{(m+M)}$

Putting the values we get

$x=\frac{200\times 10/2+50\times 10}{50+200}$

$\implies x=\frac{150\times 10}{250}$

$\implies x=6$ m

Thus, the displacement of the plank is 6 m

Hope this helps.

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Answer 2

Answer:

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