A uniform rod `OB` of length `1m`, cross-sectional areal `0.012 m^(2)` and relative density `2.0` is free to rotate about smooth hinge `O` in vertical plane. The rod is held with a horizontal string `AB` which can withstand a maximum tension of `45N`. The rod and string system is kept in water as shown in figure. The maximum value of angle `alpha` which the rod can make with vertical without breaking the string is

Options

A. `45^(@)`
B. `37^(@)`
C. `53^(@)`
D. `60^(@)`

Answer

B

Explanation

`F.B.D.` of rod `F.B.D.` :
`W = (0.012)(1)(2 xx 10^(3))(10) = 240 N`
`F_(b) = (0.012)(1)(10^(3))(10) = 120 N`
Torque about `O`
(For equilibrium
`(240 - 120)((sinalpha)/(2)) = 45(cos alpha) rArr tanalpha = (90)/(120) = (3)/(4) rArr alpha = 37^(@)`