Question

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One end of a uniform rod of mass M and length L is supported by a frictionless hinge which can withstand a tension of 1.75 Mg.The rod is free to rotate in a vertical plane .To what maximum angle should the rod be rotated from the vertical position so that when left, the hinge does not break ?​

Answer 1

Answer:

Since the reaction force at the height is not doing any work, total mechanical energy is conserved.

ΔPE=mgl/2(1−cosθ)ΔPE=mgl/2(1−cos⁡θ)

ΔK=12I0.w2ΔK=12I0.w2

=12ml23.w2=12ml23.w2

12ml2312ml23w2=mglw2=mgl. sin2θ/2. sin2⁡θ/2