Question

A rubber cord has a cross-sectional area 1 $m{m}^2$ and total unstretched length 10cm. It is stretched to 12cm and then released to project a mass of 80g. The Young's modulus for rubber is 5$\times {10}^{8}N{m}^{-2}$. Find the velocity of mass (in m/s)?

• A. 5
• B. 3
• C. 7
• D. 2

Answer 1

The correct option is A 5

$\begin{array}{c}\text{Civen,}\\ \text{cross sectional Area}\left(A\right)=1m{m}^2={10}^{-6}{m}^2\\ \text{Unstreched length}\left(L\right)=10cm=10\times {10}^{-2}m\\ \text{mass of missile}\\ \text{young modulus}\left(y\right)=5\times {10}^8{Nm}^{-2}\\ \text{Streched length}(L+\Delta L)=12cm\\ \text{Let us consider rubber cord as spring}\\ \text{then}\\ \begin{array}{cc}k& =\frac{yA}{L}\\ & =5\times {10}^{3}N/m\end{array}\end{array}$ we know, and this energy is transtered to $KE$ of missile $\begin{array}{cc}\frac{1}{2}k(\Delta L{)}^2& =\frac{1}{2}m{v}^2\\ v& =\sqrt{\frac{K}{m}}\times \Delta L\\ v& =\sqrt{\frac{5\times {10}^3}{80\times {10}^{-3}}\times 2\times {10}^{-2}}\\ & v=5m/s\end{array}$