Question

A rough uniform board of mass m
and length 2a rests on a smooth
horizontal plane and a man of mass
M walks on it from one end to the
other. Then find the distance
through which the board moves in
this line.​

Answer 1

The distance through which the board moves = 2aM/(M+m)

Step-by-step explanation:

Given:

A rough uniform board of mass m and length 2a is resting on a smooth horizontal plane, a man of mass M walks on it from one end to another

To find out:

The distance through which the board moves in  this line.

Solution:

Let the distance moved by the plank w.r.t. to the ground is d

Then the distance walked by man w.r.t. the ground will be = 2a - d

Since there is no external force acting on the system (man + plank)

Therefore, the centre of mass of the system will remain stationary

Therefore,

$0=\frac{M\times (2a-d)-m\times d}{M+m}$

$\implies (M+m)d=2aM$

$\implies d=\frac{2aM}{M+m}$

Hope this answer is helpful.

Know More:

Q: A MAN OF MASS M STANDS AT ONE END OF A PLANK OF LENGTH L WHICH LIES AT REST ON A FRICTIONLESS HORIZONTAL SURFACE. THE MAN WALKS TO THE OTHER END OF THE PLANK. IF THE MASS OF THE PLANK IS (M/3), THE DISTANCE THAT THE MAN MOVES RELATIVE TO THE GROUND WILL BE _________ A) L. B) L/4. C) 3L/4. D) L/3

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Answer 2

Answer:

Step-by-step explanation: