Q133 / 160 · AP EAMCET 2008 · Physics

A load of $1 \mathrm{~kg}$ weight is a attached to one end of a steel wire of area of cross-section $3 \mathrm{~mm}^2$ and Young's modulus $10^{11} \mathrm{~N} / \mathrm{m}^2$. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position the fractional change in length is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

  • Correct answer
    A
    $0.3 \times 10^{-4}$
  • B
    $0.3 \times 10^{-3}$
  • C
    $0.3 \times 10^{3}$
  • D
    $0.3 \times 10^{4}$

Solution

$\begin{aligned} Y & =\frac{m g l}{A \Delta l} \\ \Rightarrow \quad \frac{\Delta l}{l} & =\frac{m g}{A Y}\end{aligned}$ $\begin{aligned} \therefore \quad \frac{\Delta l}{l} & =\frac{1 \times 10}{3 \times 10^{-6} \times 10^{11}} \\ & =0.3 \times 10^{-4}\end{aligned}$

Hence, the correct answer is option: 'A'.

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