A string of $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes…
A string of $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $\frac{2}{\pi}$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then the tension in the string is
$2 M L$
$M L$
$16 M L$
$4 M L$
Solution
Given: $\omega=\frac{2}{\pi}$ rev.per sec
$\Rightarrow \omega=2 \pi \frac{2}{\pi} \mathrm{rad} / \mathrm{s}=4 \mathrm{rad} / \mathrm{s}$
The horizontal force balance reads:
$T \sin \theta=M R \omega^2$
From figure $R=L \sin \theta$
$\Rightarrow T=M L \omega^2$
On introducing, $\omega=4 \mathrm{rad} / \mathrm{s}$
$\Rightarrow T=M L(4)^2=16 \mathrm{ML}$
