Question

A wooden plank of mass 20 kg is resting on a smooth
horizontal floor. A man of mass 60 kg starts moving
from one end of the plank to the other end. The
length of the plank is 10 m. Find the displacement
of the plank over the floor when the man reaches
the other end of the plank,
-10m-
>
(A) 7.5
(C) 1.5
(B) 2.5
(D) 10


pls answer fast

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Answer 1

The displacement of the plank is 7.5 miter.

Explanation:

Suppose, the man is standing on the point 'O'. ( Refer the figure )

O is assumed as origin.

• When the man starts to move and goes to the end point M.

• If man moves x miter along positive  x- axis. Then plank moves (10-x) miter along negative x- axis.

• Since, no external force is working on the system. So, net displacement of center of mass of the system will be zero.

Therefore, we write as,

• $\dfrac{m_1\vec{r_1} + m_2 \vec{r_2}}{m_1+m_2}=0$

• Now, put the values of the variables, we get.

• $\dfrac{20(-x) + 60(10-x)}{20+80}=0$

      600 - 60x - 20x = 0

      600 - 80x = 0

       x = 7.5 miter

Thus, the displacement of the plank is 7.5 miter.