The Young's modulus of a steel wire of length \(6\,m\) and cross-sectional area \(3\,mm ^2\), is \(2 \times 11^{11}\,N / m ^2\). The wire is suspended from its support on a given planet. A block of mass \(4\,kg\) is attached to the free end of the wire. The acceleration due to gravity on the planet is \(\frac{1}{4}\) of its value on the earth. The elongation of wire is (Take \(g\) on the earth \(=10\) \(\left.m / s ^2\right):\)

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Answer & Solution

Correct Answer

(C) \(0.1\,mm\)

Step-by-step Solution

Detailed explanation

\(\text { Tension }( F )= mg\)

\(=4 \times \frac{10}{4}=10\,N\)

\(\Delta L =\frac{ FL }{ AY }\)

\(=\frac{10 \times 6}{3 \times 10^{-6} \times 2 \times 10^{11}}\)

\(=10^{-4}\,m =0.1\,mm\)

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