Question

A straight rod of negligible mass is mounted on frictionless pivot and masses $2.5kg$ and $1kg$ are suspended at distances $40cm$ and $100cm$ respectively from the pivot as shown in the above figure. The rod is held at an angle $\theta$ with the horizontal and released. Then

• A. The rod executes periodic motion about horizontal position after the release
• B. The rod remains stationary after the release
• C. The rod comes to rest in vertical position with $2.5kg$ mass at the lowest point
• D. The rod executes periodic motion about vertical position after the release

Answer 1

The correct option is B The rod remains stationary after the release

Observing the figure, we have $m_1=2.5\text{kg}$ and $m_2=1\text{kg}$

Also, it is given that $L_1=40\text{cm}$ and $L_2=100\text{cm}$

The torque exerted at the hinge due to weight of $m_1$ is $T_1=m_1\times L_1\times \cos \theta =1\text{kg m}$ (anti-clockwise)

Similarly, the torque due to weight of $m_2$ is $T_2=m_2\times L_2\times \cos \theta =1\text{kg m}$ (clockwise)

Thus, total moment at the hinge is $0$.

Clearly, the rod doesn't rotate after it is released.