A strain gage, having a gage factor of $2,$ is mounted on a rectangular steel bar $($modulus of elasticity, E

m

$$

$=200\backslash$times $10$

$$

kN$/$m

$2$

$),$ as shown in the figure given. The bar is $1\mathrm{.}5$ cm wide, $2\mathrm{.}0$ cm high and is subjected to a tensile force of $30$kN$.($a$)$ Determine the stress in the bar, the resulting strain and the resistance change of the strain gage if the resistance of the gauge was $120\backslash$Omega in the absence of the axial load. $($b$)$ Suppose that this strain gage is to be connected to a measurement device capable of determining a change in resistance with a stated uncertainty of $0\mathrm{.}005\backslash$Omega $(95\%).$ This stated uncertainty percent uncertainty in stress would result when using this resistance measure