A wooden plank of length 1m and unform cross-section is hinged at one end to bottom of a tank as shown in figure. The tank is filled with water upto a height of 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=0)`

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

B

Explanation

About hinge clcokwise torque of hinge should be equal to anti-clockwise torque of upthrust. Immersed length will be 0.5 sec `theta`.

`therefore w=((1)/(2)sin theta)=F((0.5 sec theta)/(2)) sin theta`
or `w=0.5 F sec theta " or " (1xxAxx0.5xxrho_(w)xxg)`
`=0.5(0.5 sec theta)xxAxx1.0xxrho_(w)xxgxx sec theta`
`sec^(2) theta=2 " or" theta=45^(@)`