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Question

A straight rod of negligible mass is mounted on frictionless pivot and masses 2.5 kg and 1 kg are suspended at distances 40 cm and 100 cm respectively from the pivot as shown in the above figure. The rod is held at an angle θ with the horizontal and released. Then
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A
The rod executes periodic motion about horizontal position after the release
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B
The rod remains stationary after the release
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C
The rod comes to rest in vertical position with 2.5 kg mass at the lowest point
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D
The rod executes periodic motion about vertical position after the release
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Solution

The correct option is B The rod remains stationary after the release
Observing the figure, we have m1=2.5 kg and m2=1 kg

Also, it is given that L1=40 cm and L2=100 cm

The torque exerted at the hinge due to weight of m1 is T1=m1×L1×cosθ=1 kg m (anti-clockwise)

Similarly, the torque due to weight of m2 is T2=m2×L2×cosθ=1 kg m (clockwise)

Thus, total moment at the hinge is 0.

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

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