A steel rod of length L , density d and cross-sectional area A is hinged at one end so that it can rotate freely in a vertical plane. The rod is released from a horizontal position. When it becomes ve

Question

A steel rod of length L , density d and cross-sectional area A is hinged at one end so that it can rotate freely in a vertical plane. The rod is released from a horizontal position. When it becomes vertical, the stress at its midpoint is

TestHub · Accepted Answer

Energy conservation: m g 2 L ​ = 2 1 ​ ⋅ 3 m L 2 ​ ω 2 ω 2 = L 3 g ​ Take the lower half (mass 2 m ​ , centre at 4 3 L ​ from the hinge). Let T be the tension at the midpoint. T − 2 m g ​ = 2 m ​ ω 2 ⋅ 4 3 L ​ = 8 9 m g ​ T = 8 13 m g ​ Stress = A T ​ = 8 13 d Lg ​ (using m = d A L )

Physics - Elasticity Question with Solution | TestHub

Options:

Doubts & Discussion