Question

A rubber cord of length 10 cm is stretched upto 12 cm. If cross sectional area of cord is 1 $m{m}^2$, find the velocity of a missile (mass 5g) which is hit upon with this rubber cord. ($Y_{rubber}=5\times {10}^{8}N/m^2$)

• A. 10 m/s
• B. 20 m/s
• C. $\frac{15}{3}$ m/s
• D. 8 m/s

Answer 1

The correct option is B 20 m/s

$\begin{array}{cc}& \begin{array}{cc}\Delta l& =12-10=2cm\end{array}\\ & \begin{array}{cc}m& =5g,\\ & Y=5\times {10}^8\end{array}\\ F& =\frac{YA\Delta L}{L}\end{array}$

$\text{Area of cross section}=1{mm}^2$

$\begin{array}{c}F=\frac{YA\Delta L}{L}\\ F=\frac{5\times {10}^8\times {10}^{-6}\times 2}{10}={10}^2\\ \text{Energy}=\frac{1}{2}\times F\times \Delta L=\frac{1}{2}m{\nu }^2\\ \Rightarrow \frac{1}{2}\times 100\times 2\times {10}^{-2}=\frac{1}{2}\times 5\times {10}^{-3}{v}^2\\ V^2=\frac{2\times {10}^3}{5}\\ V=20m/s\end{array}$