A load is suspended from a steel wire with a radius of 1mm. The load extends the wire the same amount as does heating by `20^(@)C`. Find the load (approx). `alpha_("steel") = 1.1 xx 10^(-5) K^(-1)`, Young's modulus `= 21.6 xx 10^(10) N//m^(2)`

Answer

15.24

Explanation

Increase of length on heating=` l alpha t`
Strain `=(l alpha t)/(l)=alpha t =1.1 xx 10^(-5) xx 20 =2.2 xx 10^(-4)`
`therefore` stress = Y `xx` strain `=21.6 xx 10^(10)xx2.2 xx 10^(-4)=21.6 xx 2.2 xx 10^6 N//m^2`
`therefore` mass of the load applied = stress `xx` area of cross section
`=21.6 xx 2.2 xx 10^6xx(pi r^2)=21.6 xx 2.2 xx 10^6xx(22)/(7)xx((1)/(10^3))^2`
`=21.6 xx 2.2 xx (22)/(7) N=(21.6 xx 2.2 xx 22)/(7 xx 9.8)` kg =15.24 kg