Two fines steel wires , fastened between the projectors of a heavy brass bar, are just taut when the whole system is at `0^(@)C`. What is the tensile stress in the steel wires the temperature of the system is raised by `200^(@)C`? (`alpha_("glass") = 2 xx 10^(-5) ^(@)C ^(-1), alpha_("steel") = 1.2 xx 10^(-5)"^(@)C^(-1), Y_("steel") = 200GNm^(-2)`)

Options

A. `3.2 Nm^(-2)`
B. `3.2 xx 10^(8) Nm^(-2)`
C. `32 xx 10^(8) Nm^(-2)`
D. `0.48 Nm^(-2)`

Answer

B

Explanation

Tensile Stress
= `(Y_(steel))((Deltal)/(l)) = Y_(S) (alpha_(b)-alpha_(S))DeltaT`
=` 200 xx 10^(9)(0.8 xx 10^(-5)) (200) = 3.2 xx 10^(8) Nm^(-2)`
=`0.32 GNm^(-2)`