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)`

Options

A. `5 kg`
B. `10 kg`
C. `15 kg`
D. `20 kg`

Answer

C

Explanation

Increase of the 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)`
`:.` Stress `= Y xx` starin
`= 21.6 xx 10^(10) xx 2.2 xx 10^(-4)`
`21.6 xx 2.2 xx 10^(6) N//m^(2)`
`:.` mass of load applied `=` stress `xx` area of cross section
`= 21.6 xx 2.2 xx 10^(6) xx (pir^(2))`
`= 21.6 xx 2.2 xx 10^(6) xx (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`