1 Q.A line was measured with a steel tape which is exactly 30 m long at 18°C and found to be 452.3.43 m. The temperature during measurement was 32°C. Find the true length of line Take coefficient of expansion of tape per °C = 0.000117
Solution:
Given data:
Length of tape L = 30m
Coefficient of thermal expansion = α = 0.0000117
Temperature at which the tape is standardized = T = 18 ° C
Mean temperature in the field during measurement,
Tm = 32 °C
Correction for temperature
= Ct= α(Tm – T) * L
= 0.0000117(32 – 18) * 30
= 0.004914 m
The length of the tape at 32° C
= 30 + Ct
L’ = 30 + 0.004914
= 30.004914m
Measured length of a line = 452.343 m
True Length of a line
=(L’/ L ) x measured length
=(30.004914/30) * 452.343
= 452.417m
True length ofa line = 452.417m
2Q. The area of the plan of an old survey plotted to a scale of 20 metres to 1 cm measures now as 125.6 sq. cm as found by planimetre. The plan is found to have shrunk, so that a line originally 10 cm long now measures 9.6 cm only. There was also a note on the plan that the 20 m chain used was 6 cm too short. Find the true area of the field.
Solution:
Present 9.6 cm is equivalent to 10 cm original length
therefore Present area of 125.6 sq. cm is equivalent to original area of field on the map
=(10/9.6) ² x 125.6
= 136.28 sq .cm
According to the scale of plan
Icm = 20n
1cm²= 20 ×20 = 400m²
Hence the actual area of the field.
A’ = 136.28 × 400
= 54, 512 m²
But the 20 m chain used was 6 cm, too short.
Incorrect length of the chain
L’= 20 – 0.06 = 19.94m
Therefore true area of the field
A =( L’/ L )² x measured area
=(19.94/20) ² × 54.512
=54. 187m² or 5.4187 hectares.
true Area of field = 54.187m²