A load of 4 kg is suspended from a ceiling through a steel wire of length 2 m and radius 2 mm. It is found that the length of the wire increase by 0.032 mm as equilibrium is achieved. What would be the Young's modulus of steel ? (Take , `g=3.1 pi m s^(-2)`)

Options

A. `2.0 xx 10^(11) Nm^(-2)`
B. `2.82 xx 10^(11) Nm^(-2)`
C. `0.20 xx 10^(11) Nm^(-2)`
D. `0.028 xx 10^(11) Nm^(-2)`

Answer

A

Explanation

(a) Given, mass of load = 4 kg
Length of wire, l=2 m
Radius of wire (cross-section)`=2 mm = 2 xx 10^(-3)` m
and change in length, `Deltal=0.031xx 10^(-3) m`
Young's modulus,
`Y=("Stress")/("Strain")=((mg)/(A))/(((Deltal)/(l)))=((4xx3.1pi)/(pi(2xx10^(-3))^(2)))/((Deltal//l))`
`implies Y=(4xx3.1pi)/(pixx4xx10^(-6))xx(2)/(0.031xx10^(-3))`
`=(3.1xx2)/(0.031)xx10^(9)=2xx10^(11) Nm^(-2)`