Question

A steel tape 20 m long standardised at ${55}^{\circ }$ F with a 10 kg pull was used for measuring a base line. If temperature at the time of measurement was ${80}^{\circ }F$ and the pull exerted was 16 kg. Weight of 1 cubic cm of steel = 7.86 g, weight of tape = 0.8 kg, E = $2.109\times {10}^{6}kg/c{m}^2$. Coefficient of expression of tape per $1^{\circ }F=6.2\times {10}^{-6}$. The correction per tape will be

• A. 6.30 mm
• B. 3.56 mm
• C. 4.22 mm
• D. 2.14 mm

Answer 1

The correct option is D 2.14 mm

Correction for temperature

= $20\times 6.2\times {10}^{-6}\times (80-55)$

= 0.0031 m = 3.1 mm (+ve)

Correction for pull,
$\left(C_p\right)=\left(\frac{P-P_0}{AE}\right)\times L$

Weight of tape,
$0.8=A\times (20\times 100\times (7.86\times {10}^{-3}\left)\right)$

$A=\frac{0.8}{7.86\times 2}=0.051sq.cm$

$C_p=\frac{(16-10)\times 20}{0.051\times 2.109\times {10}^6}$

$C_p=0.00112m=1.12mm(+ve)$

$Correctionofsag=\frac{W^{2}l}{24P^2}$

$=\frac{20(0.8{)}^2}{24(16{)}^2}=0.00208m$

= 2.08 mm (-ve)

total correction = 3.1 + 1.12 - 2.08 = 2.14 mm (+ve)