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Q.

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

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a

3.0 x 10^-2 mm

b

6.06 x 10^-2 mm

c

6.9 x 10^-2 mm

d

2.77 x 10^-2 mm

answer is C.

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Detailed Solution

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$e = \frac{Fl}{Ay}$
Both are steel. So y is same force is same So F is same.
$\begin{array}{l} So, \frac{e_{B}}{e_{A}} = \frac{l_{B}}{l_{A}} \cdot \frac{A_{A}}{A_{B}} \\ = \frac{2 l}{l} \cdot \frac{D^{2}}{(2.4 D)^{2}} = \frac{2}{(2.4)^{2}}, e_{B} = \frac{2}{(2.4)^{2}} (0.2) mm \end{array}$
= 6.9 x 10^-2 mm

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