Please solve ot step by step

Solution

Now as we need to find tension at mid point
Putting x  = l/2
$T =\frac{m{\omega }^2}{2l}\left[l^2 -\frac{l^2}{4}\right] =\frac{m{\omega }^2}{2l}\left[\frac{2l^2}{4}\right] =\frac{m{\omega }^{2}l}{4}$