In the determination of Young's modulus $\left(Y=\frac{4 MLg }{\pi / d ^2}\right)$ 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 $\ell=0.25 \ mm$ in the length of the wire is observed. Quantities $d$ and $\ell$ 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

  • [IIT 2012]
  • A

    due to the errors in the measurements of $d$ and $\ell$ are the same.

  • B

    due to the error in the measurement of $d$ is twice that due to the error in the measurement of $\ell$.

  • C

    due to the error in the measurement of $\ell$ is twice that due to the error in the measurement of $d$.

  • D

    due to the error in the measurement of $d$ is four time that due to the error in the measurement of $\ell$.

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