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Physics Class 12th Mechanical Properties of Solids Physics NCERT Exemplar Solutions Class 12th Chapter Nine

In an experiment to determine the Young’s modulus of wire of a length exactly 1m, the extension in the length of the wire is measured as 0.4mm with an uncertainty of $\pm$ 0.02mm when a load of 1kg is applied. The diameter of the wire is measured as 0.4mm with an uncertainty of $\pm$ 0.02mm. The error in the measurement of Young’s modulus $(Δ Y)$ is found to be x × 10¹⁰Nm^-2. The value of x is _________.

(take g = 10 ms^-2)

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Vishal Baghel | Contributor-Level 10

2 months ago

L = 1 m

$Δ L = 0.4 \times 1 0^{- 3} m$

$m = 1 k g$

d = 0.4 × 10^-3 m

$\frac{F}{A} = y \frac{Δ L}{L}$

$y = \frac{F L}{A Δ L} = \frac{(m g) \times 1}{(\frac{π d^{2}}{4}) \times 0.4 \times 1 0^{- 3}}$

$Δ y = 0.1 \times 0.199 \times 1 0^{12} = 1.99 \times 1 0^{10}$

= 1.99

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