base line was measured in catenary as shown below, with a tape of nominal length $30$m $.$ The tape measured $30\mathrm{.}015$m when standardized in catenary at $20$C and $5$kgf tension. If the mean reduced level of the base was $30\mathrm{.}50($m$)/($O$)$O D $,$ calculate its true length at mean sea level. Given: weight per unit length of tape $=0\mathrm{.}03$k$($g$)/($m$)($w$)$ ; density of steel $=7690$k$($g$)/($m$)3()$; coefficient of expansion $=11\backslash$times $10-6$ per C;E$=210\backslash$times $103($N$)/($m$)$m$2$; gravitational acceleration g$=9\mathrm{.}80665($m$)/($s$)2$ ; radius of the Earth $=6\mathrm{.}4\backslash$times $106$m$($R$).$