One end of a uniform wire of length `'L'` and mass `'M'` is attached rigidly to a point in the roof and a load of a mass `'m'` is suspended from its lower end. If `A` is the area of cross-section of the wire then the stress in the wire at height `'x'` from its lower end `(x lt L)` is

Options

A. `(Mg)/(A) + (mxg)/(AL)`
B. `(mg)/(A) - (Mxg)/(AL)`
C. `(mg)/(A) + (Mxg)/(AL)`
D. `(mg)/(AL) + (Mxg)/(A)`

Answer

C

Explanation

Tension in the string at point `'P'` is
`TY = wt` of load `+ wt` of wire of length `'x'`
`T = mg + (M)/(L) xg`, Stress at `P = (T)/(A) = (mg)/(A) + (Mxg)/(AL)`