In the determination of young’s modulus $Y = \frac{4 M L g}{{πld}^{2}}$ by using Searle’s method, a wire of length L = 2m and diameter 0.5mm is used. For a load of M = 2.5 kg an extension of l = 0.25mm in the length of the wire is observed. Quantities ‘d’ and ‘l’ are measured using screw gauge and micrometer respectively. They have the same pitch of 0.5mm.The number of divisions of their circular scale is 100. The contribution to the maximum possible error of the Y measurement is

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due to the error in the measurement of ‘d’ is four times that the due to the error in the measurement of ‘l’

due to errors in the measurements of ‘d’ and ‘l’ are same

due to errors in the measurements of d is twice that due to the error in the measurement of ‘l’

due to the error in the measurement of ‘l’ is twice that due to the error in the measurement of ‘d’

answer is A.

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Detailed Solution

errors due to measurement of d $2 \frac{∆ d}{d} = 2 \frac{0.5 \times 10^{- 2}}{0.5} = 2 \times 10^{- 2}$

error due to measurements of l $\frac{∆ l}{l} = \frac{0.5 \times 10^{- 2}}{0.25} = 2 \times 10^{- 2}$

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