The uniform `120 N` board shown in figure is supported by two ropes. A `400 N` weight is suspended one-fourth of the way from the left end. Choose the correct options

Options

A. `T_(1)=185N`
B. `T_(2)=371N`
C. `T_(2)=185N`
D. `tan theta=0.257`

Answer

A, B, D

Explanation

Taking moments about the left edge and resolving `T_(1)` into `x` and `y` components,
`sum tau=0` yields `LT_(1) cos 30^(@)-(0.25 L)(400)`
`-(0.5 L)(120)=0`
Dividing throught by `L` and solving, we get `T_(1)=185 N` Substituting into our earlier equations, we get
`T_(1)=185 N`
`T_(2) = sin theta=92.5 N` and `T_(2)=cos theta=360 N`
Dividing the equations yields
`tan theta=0.257, `or `theta=14.4^(@)`
Than `0.249 T_(2)=92.5` and `T_(2)=371 N`
One can always chek moment problem results by taking moments about another point, such as the right end of the bar for this problem