A block of mass M is tied to one end of a mas | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the displacement of the plank relative to the ground be $x$ in the left direction. Since the system is on a smooth surface and there are no ex

Vedclass · Accepted Answer

$0.6$

Vedclass · Answer

(B) Let the displacement of the plank relative to the ground be $x$ in the left direction. Since the system is on a smooth surface and there are no external horizontal forces,the position of the center of mass of the system remains unchanged.Let the mass of the block be $m_1 = M$,the mass of the man be $m_2 = 2M$,and the mass of the plank be $m_3 = 2M$. The total mass of the system is $M_{total} = M + 2M + 2M = 5M$.The displacement of the center of mass is zero: $\Delta X_{cm} = \frac{m_1 \Delta x_1 + m_2 \Delta x_2 + m_3 \Delta x_3}{M_{total}} = 0$.Let the displacement of the plank be $x$ to the left $(-x)$.The man is on the plank,so his displacement is also $-x$.The block is initially $3 \ m$ away from the pulley. When it reaches the pulley,it has moved $3 \ m$ relative to the plank to the right. Its displacement relative to the ground is $\Delta x_1 = (3 - x)$ to the right.Substituting these values: $M(3 - x) + 2M(-x) + 2M(-x) = 0$.$3M - Mx - 2Mx - 2Mx = 0$.$3M = 5Mx$.$x = \frac{3}{5} = 0.6 \ m$.

Similar Questions

Two bodies of masses $2 \ kg$ and $4 \ kg$ are moving with velocities $20 \ m/s$ and $10 \ m/s$ towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass (in $m/s$)?

$A$ man of mass $M$ stands at one end of a plank of length $L$ which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $3M$,the distance that the man moves relative to the ground is:

In the given figure,if the speed given to block $A$ is $10\,m/s$ and block $B$ is initially at rest,then the speed of the centre of mass after $10\,s$ will be ....... $m/s$.

$A$ man weighing $80\, kg$ is standing at the centre of a flat boat and he is $20\, m$ from the shore. He walks $8\, m$ on the boat towards the shore and then halts. The boat weighs $200\, kg$. How far is he from the shore at the end of this time?

Vedclass Test Series

Exam Paper Generator

Online Exam Module