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 $5$

$\text{Tension in cord}=\frac{YA}{L}\Delta l$

$=\frac{5\times {10}^8\times 1\times {10}^{-6}\times 2\times {10}^{-2}}{10\times {10}^{-2}}=100N$

$\text{When mass is released, stored elastic energy}=\text{Kinetic energy of mass}$

$\Rightarrow \frac{1}{2}F\times \Delta l=\frac{1}{2}m{v}^2$

$v=\sqrt{\frac{F\times \Delta l}{m}}=\sqrt{\frac{100\times 2\times {10}^{-2}}{80\times {10}^{-3}}}=5\text{m/s}$