$($c$)$ A simple force transducer is illustrated in Figure Q$1($c$).$ A round steel bar, $0\mathrm{.}02m$ in diameter and $0\mathrm{.}40m$ in length, is subjected to a tensile force, $F$ of $33,000kg,$ where the steel Young Modulus, $E=2{10}^{12}k\frac{g}{m^2}.$

$($i$)$ Calculate the elongation of the round steel bar, $L,$ in meters.

$(4$ marks$)$

$($ii$)$ Calculate the strain.

$($iii$)$ Given that the strain gauge with a gauge factor of $2$ is fastened to the round steel bar and the original resistance value of the gauge is $130.$ Calculate it's change in resistance if a strain obtained in Q$1($c$)($ii$)$ is observed.

$($iv$)$ Using the same strain gauge stated in Q$1($c$)($iii$),$ sketch an electrical circuitry deploying Wheatstone Bridge to measure the force. $($Propose the suitable values

Figure Q$1($c$)$for all resistors.$)$