Question

When the load on a wire is increased from $3kg-wt$ to $8kg-wt$, the elongation increases from $0.61mm$to $1.02mm$ . The required work done during the extension of the wire, is

• A. $16\times {10}^{-3}J$
• B. $8\times {10}^{-2}J$
• C. $20\times {10}^{-2}J$
• D. $31\times {10}^{-3}J$

Answer 1

The correct option is D $31\times {10}^{-3}J$

$\begin{array}{cc}& \Delta l_1=0.61mm\Delta l_2=1.02mm\\ & \text{(work done)}=\bigcup _1-\bigcup _2\dots ..\left(i\right)\end{array}$

$\begin{array}{cc}U& =\frac{1}{2}\times \text{stress}x\text{strain}x\text{volume}\\ & =\frac{1}{2}\times \frac{F}{A-1}\times \frac{\Delta L}{-L}\times A\cdot K\\ U& =\frac{1}{2}\times F\times \Delta L\end{array}$

$\begin{array}{cc}{U}_1& =\frac{1}{2}\times 3\times 10\times 0.61\times {10}^{-3}\\ & =9.15\times {10}^{-3}J\\ & =\text{work done dussing}\\ & \text{case}1\end{array}$

$\begin{array}{cc}{U}_2& =\frac{1}{2}\times 8\times 10\times 1.02\times {10}^{-3}\\ U_2& =40.8\times {10}^{-3}J\\ =& \text{work done during}\\ & \text{case II}\end{array}$

$\begin{array}{ccc}(\text{work done)}& U_2-U_1\text{during case II to case}1& =(40.8-9.15)\times {10}^{-3}J\\ & =31.65\times {10}^{-3}J& \end{array}$