In an experiment on the determination of Young’s Modulus of a wire by Searle’s method, following data is available. (don’t consider significant figures)
Normal length of the wire L=110 cm
Diameter of the wire d = 0.01 cm
Elongation in the wire l=0.125 cm
This elongation is for a tension of 50 N. The least counts for L,d and l are 0.01 cm, 0.00005 cm and 0.001 cm respectively. Calculate the maximum percentage error nearest to an integer in calculating the value of Young’s modulus (Y)

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Detailed Solution

$Y = \frac{S t r e s s}{S t r a i n} = \frac{T / A}{l / L} \Rightarrow Y = \frac{T L}{A l} = \frac{4 T L}{π d^{2} l}, \frac{Δ Y}{Y} = \frac{Δ L}{L} + \frac{Δ l}{l} + 2 \frac{Δ d}{d}$

Since $\frac{4 T}{π}$ is a constant, so it does not contribute anything to the net error.

$\Rightarrow \frac{Δ Y}{Y} = \frac{0.01}{110} + \frac{0.001}{0.125} + 2 (\frac{0.00005}{0.01}) \Rightarrow \frac{Δ Y}{Y} \times 100 % = 0.009 + 0.8 + 1 = 1.809 %$