In the determination of Young’s modulus ( Y = 4 MLg ~d ^ 2 ) by using Searle’s method, a…
Physics · JEE Main · NTA Exams — Physics and Measurement
In the determination of Young’s modulus \(\left(\mathrm{Y}=\frac{4 \mathrm{MLg}}{\pi \ell \mathrm{~d}^{2}}\right)\) 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 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, repectively. 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 is
- due to the errors in the measurements of d and l are the same
- due to the error in the measurement 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.
- due to the error in the measurement of d is four times that due to the error in the measurement of l.
Answer
(D) due to the error in the measurement of d is four times that due to the error in the measurement of l .
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