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

Options

A. `(13dLg)/(8)`
B. `(12dLg)/(8)`
C. `(2dLg)/(5)`
D. `(dLg)/(2)`

Answer

B

Explanation

Pressure at point 1
`P_(1)=P_(atm)+rhog(2h)`
Applying Bernoulli's theorem between points 1 & 2
`P_(atm)+rhog(2h)+2rhogh = P_(atm)+(1)/(2)(2rho)V^(2)=V^(2)=4gh`
`V = 2 sqrt(gh)`