A rubber cord of length 10 cm is stretched upto 12 cm. If cross sectional area of cord is 1 $$mm^2$$, find the velocity of a missile (mass 5g) which is hit upon with this rubber cord. ($$Y_{rubber} = 5 \times 10^8 \ N/m^2$$)
Correct option is B. 20 m/s
$$\begin{aligned}\text { } & \begin{aligned}\Delta l&=12-10 {= 2~cm}\end{aligned}\\&\begin{aligned}m&=5\mathrm{~g},\mathrm{~}\\&Y=5\times10^{8}\end{aligned} \\F &=\frac{Y A \Delta L}{L}\end{aligned}$$
$$\text { Area of cross section }=1\mathrm{~mm}^{2}$$
$$\begin{array}{l}F=\frac{Y A \Delta L}{L}\\F=\frac{5\times 10^{8} \times 10^{-6} \times 2}{10}=10^{2} \\\text { Energy }=\frac{1}{2} \times F\times \Delta L=\frac{1}{2} m\nu^{2}\\\Rightarrow\frac{1}{2} \times 100 \times 2\times 10^{-2}=\frac{1}{2} \times 5 \times 10^{-3}v^{2} \\V^{2}=\frac{2 \times 10^{3}}{5}\\V=20\mathrm{~m} / \mathrm{s}\end{array}$$