Question

A steel wire has length 2.0 m, radius 1 mm and $Y=2\times {10}^{11}N/m^2$ A sphere of mass 1 kg is attached at one end of the wire which is then whirled in a vertical circle with speed 2 rev/sec. Elongation of the wire when mass is at the lowest position.

• A. 1.0 mm
• B. 2.0 mm
• C. 0.1 mm
• D. 0.01 mm

Answer 1

The correct option is A 1.0 mm

$\begin{array}{c}\text{Given, lure of length}=2m\\ \text{radius}=1mm\\ y=2\times {10}^{11}N/m^2\\ \text{sphere of mass}=1kg\\ \text{frequency}=2\end{array}$

$\begin{array}{cc}T-mg& =m{\omega }^{2}R\\ T=& mg+m{\omega }^{2}R\\ =& 10+16{\pi }^2\left(2\right)\\ & =325N\\ T=& YA\left(\frac{\Delta L}{L}\right)\\ \frac{325\times \left(2\right)}{2\times {10}^{11}\times \pi \left({10}^{-6}\right)}& =\Delta L\\ \therefore & \Delta L=1mm\end{array}$