Q1: If 50 m point of a 100 m tape is 50 cm off line, and 50 m sections are straight, an error is generated equal to

ANS:C -

Error =h^2/2*L.
For L= 50m and h= 0.5m , the error = 1/400.
Therefore error per unit length of 50m (as the rest part of the chain is straight) equals 1/(400*50) = 1/20,000. The answer should be 1/40000.
For 50m length is 50.025,
And next 50 m is straight so it is 0.025/100. True length upto 50 m portion is √50^2+0.5^2 = 50.0025.
Error = 50.0025-50= 0.0025.
for 100 m length error = 0.0025*2=0.0050.
Error for 100 m= 0.005/100=1/20000. True length upto 50m portion is
√(50^2 + 0.5^2) = 50.0025.

So error is 50 - 50.025 = 0.025 m in 50 m length.
50 m length error is 0.025 m.

So in 100 m length error is 0.025 * 2 = 0.05 m,
So error is 0.05/100 = 1/20,000.