Question

A rod of length l and mass m hinged at one end is released from rest from vertical position

Answer 1

The angular velocity of the rod when  it is in vertical position is w=√3g/L

Explanation:

Correct statement:

A rod of length l is hinged from one end . it is brought to a horizontal position and released. the angular velocity of the rod when it is vertical position is

Given:

This question can be solved by taking center of mass.

Length of rod = l/2 (length at centre of mass)

Now if the body changes it's state of motion then the potential and kinetic energy would be equal.

Potential energy = kinetic energy

Now mass of rod =  M

MgL/2=1/2 Iw²

MgL = (ML²/3)w²

By substituting the value of momentum of inertia of rod.

w=√3g/L

where w= angular velocity of rod

I =  moment of inertia of rod

Thus the angular velocity of the rod when  it is in vertical position is w=√3g/L

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Answer 2

Explanation:

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