Question

One end of a string of length $L$ and cross-sectional area $A$ is fixed to a support and the other end is fixed to a bob of mass $m$. The bob is revolved in a horizontal circle of radius $r$ with an angular velocity $\omega$ such that the string makes an angle $\theta$ with the vertical. The stress in the string is :

• A. $\frac{mg}{A}$
• B. $\frac{mg}{A}(1-\frac{r}{L})$
• C. $\frac{mg}{A}(1+\frac{r}{L})$
• D. none of these

Answer 1

The correct option is D none of these

Stress$=\frac{T}{A}$
$=\frac{mg}{Acos\theta }$ (on taking the component in the string direction)
where $cos\theta =\frac{\sqrt{L^2-r^2}}{L}$
$=\sqrt{1-\frac{r^2}{L^2}}$
Stress$=\frac{mg}{A\sqrt{1-\frac{r^2}{L^2}}}$