A uniform rod OB of length 1m, cross-sectional area `0.012 m^(2)` and relative density 2.0 is free to rotate about O in vertical plane . The rod is held with a horizontal string AB which can withstand a maximum tension of 45 N. 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

A uniform rod ………….
`F.B.` of rod :
`W = (0.012) (1) (2xx10^(3)) (10) = 240 N`
`F_(b) = (0.012) (1) (10^(3)) (10) = 120N`
Torque about `O` :

(For equilibrium)
`(240 - 120) ((sin alpha)/(2)) = 45 (cos alpha)`
`implies tan alpha = (90)/(120) = (3)/(4) impliesalpha 37^(@)`