JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100\) N is applied to the wire, the extension in length is \(0.5\) cm, measured by a micrometer of least count \(0.001\) cm. The error in the measured Young's modulus is \(\alpha \times 10^9\) N/m\(^2\). The value of \(\alpha\) is _______.
(Ignore the contribution of the load to Young's modulus error calculation)
- A \(1.3\)
- B \(1.65\)
- C \(0.13\)
- D \(0.25\)
Answer & Solution
Correct Answer
(B) \(1.65\)
Step-by-step Solution
Detailed explanation
The formula for Young's modulus is given by: \(Y = \dfrac{F L_0}{A \Delta L} = \dfrac{4 F L_0}{\pi d^2 \Delta L}\) Substituting the given values into the formula: \(Y = \dfrac{4 \times 100 \times 1.5}{\pi \times (0.08 \times 10^{-2})^2 \times (0.5 \times 10^{-2})}\)…
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