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A uniform rod OB of length 1m, cross-sec...

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

A

`45^(@)`

B

`37^(@)`

C

`53^(@)`

D

`60^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
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^(@)`
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