(d) When the string makes an angle $\theta$ with the vertical, then
$T - mg\ cos\ \theta = \frac{mv^{2}}{r}$
Substituting the values, we obtain
$6 - (1)(10)\cos{\theta = \frac{1 \times (4)^{2}}{1}}$
or $6 - 10$ $cos\ \theta$=16
or $cos\ \theta = - 1 = \cos{180{^\circ}}$
$\therefore\ = 180{^\circ}$