A wooden plank of length 1m and uniform cross-section is hinged at one end to the bottom of a tank as shown in fig. The tank is filled with water upto a hight 0.5m. The specific gravity of the plank is 0.5. Find the angle `theta` that the plank makes with the vertical in the equilibrium position. (Exclude the case `theta=theta^@`)

Options

A. `45^(@)`
B. `60^(@)`
C. `30^(@)`
D. `37^(@)`

Answer

A

Explanation

Taking moments of all forces about point `O`. Moment of hinge force will be zero.
Moment of W (c.w)`=` moment of `F(A.C.W)`
`:. (Algrho)(1)/(2)sintheta=A(0.5sectheta)(rho_(w))(g)((0.5sectheta)/(2))sintheta`
`impliestheta=45^(@)`