Question

In the determination of Young's modulus $(\gamma =\frac{4MLg}{\pi l{d}^2})$ by using Searle's method, a wire of length $L=2m$ and diameter $d=0.5mm$ is used. For a load $M=2.5kg$, an extension $l=0.25mm$ 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 $0.5mm$. 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
• B. Due to the errors in the measurement of $d$ is twice that due to the error in the measurement of $l$
• C. Due to the errors in the measurement of $l$ is twice that due to the error in the measurement of $d$
• D. Due to the errors in the measurement of $d$ is four times that due to the error in the measurement of $l$

Answer 1

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 $l$

$\frac{d\mu }{\mu }=\frac{dM}{M}+\frac{dL}{L}+\frac{dg}{g}+\frac{dl}{l}+\frac{2dd}{d}$

$\therefore$ Error in d have twice contribution than error in $l$