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  •  A force is applied to a steel wire , rigidly clamped at one end. As a result elongation

 A force is applied to a steel wire \mathrm{'A'}, rigidly clamped at one end. As a result elongation in the wire is 0.2 \mathrm{~mm}. If same force is applied to another steel wire '\mathrm{B}'of double the length and a diameter 2.4 times that of the wire 'A', the elongation in the wire '\mathrm{B}'will be (wires having uniform circular cross sections)

Option: 1

6.06 \times 10^{-2} \mathrm{~mm}


Option: 2

2.77 \times 10^{-2} \mathrm{~mm}


Option: 3

3.0 \times 10^{-2} \mathrm{~mm}


Option: 4

6.9 \times 10^{-2} \mathrm{~mm}


Answers (1)

best_answer

\mathrm{Y}=\frac{\mathrm{F} \ell}{\mathrm{A} \Delta \ell}
\mathrm{F}=\frac{\mathrm{YA} \Delta \ell}{\ell}

\left(\frac{\mathrm{A} \Delta \ell}{\ell}\right)_{1}=\left(\frac{\mathrm{A} \Delta \ell}{\ell}\right)_{2}

\frac{\Delta \ell_{2}}{\Delta \ell_{1}}=\frac{\mathrm{A}_{1}}{\mathrm{~A}_{2}} \times \frac{\ell_{2}}{\ell_{1}}
\frac{(\Delta \ell)_{2}}{0.2}=\frac{1}{2.4 \times 2.4} \times \frac{2}{1}

(\Delta \ell)_{2}=6.9 \times 10^{-2} \mathrm{~mm}

 

Posted by

jitender.kumar

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