Question

A person of mass m is standing on one
plank of mass Mand length Land floating
The person moves from one end to another and
stops. The displacement of the plank is –
Lm
(2) Lm(M + m)
(1) (m+ M)
(M + m)
Lm
LM
(4) (m + M)​

Answer 1

Answer:

(a) Lm/(m+M)

Explanation:

Let displacement of plank is x Let velocity of person wrt. plank is v and velocity of plank is opposite direction is V. According to law of conservation of momentum mv = (m + M)V or mL/t = (M + m) x (x/t) where t is time of motion x = mL/(m+M)

Answer 2

Answer:

The displacement of the plank is Lm/M + m

Explanation:

Given ;-

         Mass of person = m

         Mass of plank = M

         Length of plank = L

Let the displacement of the plank be x.

Now;-

Since the surface is smooth, so as the man applies force on the plank forward, the plank applies a force on surface backwards making it to displace by few units. Let the displacement be z here.

Now, since no external force is acting on the system ( man + plank ), so, the centre of mass will remain stationary and won't change its position. And we know that, when centre of mass is stationary moment of mass on the two sides is equal. So;

                m₁Δx₁ (Man) = m₂Δx₂ (Plank)

So, putting the given values, we get;-

                         (L - x)m = Mx

                        Lm - xm = Mx

                                Lm = Mx + mx

                                Lm = (M + m)x

                                x = Lm / M + m

Hence, the displacement of the plank is Lm/M+m units.

Hope it helps! ;-))