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# When the weight on a string is changed from 4Kg to 10Kg,the elongation changes from 0.3mm to 0.7mm,how much work done during this extension of the string?($g=10m/s^2$)

$\begin{array}{1 1}(A)\;41mJ\\(B)\;29mJ\\(C)\;20.5mJ\\(D)\;\text{None of above}\end{array}$

As the elastic energy of string E =$\large\frac{1}{2}$$\times force\times extension Work of string=E_2-E_1 \Rightarrow \large\frac{1}{2}$$\times 10\times 10\times .7\times 10^{-3}$$-\large\frac{1}{2}$$\times 4\times 10\times 10^{-3}\times .3$
$\Rightarrow \large\frac{1}{2}$$\times (7-1.2)\times 10^{-2} \Rightarrow \large\frac{5.8}{2}$$\times 10^{-2}$
$\Rightarrow 2.9\times 10^{-2}J$
$\Rightarrow 29mJ$
Hence (B) is the correct answer.