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))

A load of 4 kg is suspended from a ceiling through a steel wire of len

1.	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))
Answer» `2.0 xx 10^(11) Nm^(-2)` `2.82 xx 10^(11) Nm^(-2)` `0.20 xx 10^(11) Nm^(-2)` `0.028 xx 10^(11) Nm^(-2)` Solution :(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)`