Question

Steel rod of length L density D and cross section area is held at one end so that it can rotate freely in a vertical plane the rod is released from horizontal position when it becomes vertical the stress at the its midpoint is
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Answer 1

• The stress at its mid point is 13mg/8 or 13dLg/8

Given-

Length of the steel rod = L

Density of the steel rod = D

To calculate the stress at the mid point. We know that

Torque = moment of inertia × angular acceleration

By applying the above concept we get -

mg/2 = 1/2 × ml² ω² / 3

ω = $\sqrt{\frac{3g}{L} }$

T - m/2g = mω² / 2 × 3L/4 where T is the tension or the vertical stress, m is mass, ω is angular velocity and L is the length. Mass can be written in the form of density also.

So, T = mg/2 + 3/8 × 3mg = 13mg /8 = 13dLg/8

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