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Question

In the determination of Young's modulus $$\left (\gamma = \dfrac {4MLg}{\pi ld^{2}}\right )$$ by using Searle's method, a wire of length $$L = 2\ m$$ and diameter $$d = 0.5\ mm$$ is used. For a load $$M = 2.5\ kg$$, an extension $$l = 0.25\ mm$$ in the length of the wire is observed. Quantities $$d$$ and $$l$$ are measured using a screw gauge and a micrometer, respectively. They have the same pitch of $$0.5\ mm$$. The number of divisions on their circular scale is $$100$$. The contributions to the maximum probable error of the $$Y$$ measurement.


A
Due to the errors in the measurement of d and l are the same
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B
Due to the errors in the measurement of d is twice that due to the error in the measurement of l
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C
Due to the errors in the measurement of l is twice that due to the error in the measurement of d
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D
Due to the errors in the measurement of d is four times that due to the error in the measurement of l
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Solution

The correct option is B Due to the errors in the measurement of $$d$$ is twice that due to the error in the measurement of $$l$$
$$\cfrac{d\mu}{\mu}=\cfrac{dM}{M}+\cfrac{dL}{L}+\cfrac{dg}{g}+\cfrac{dl}{l}+\cfrac{2dd}{d}$$
$$\therefore$$ Error in d have twice contribution than error in $$l$$

Physics

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