Answer
(a) $T=3mg$
(b) Please see the work below.
Work Step by Step
(a) According to law of conservation of energy
$U_i+K_i=U_f+K_f$
$\implies mgl+0=0+\frac{1}{2}mv^2$
$\implies v^2=2gl$
We know that
$\Sigma F_y=ma_{cp}$
$\implies T-mg=\frac{mv^2}{r}$
$\implies T=m(g+\frac{v^2}{l})$
$T=m(g+\frac{2gl}{l})$
$T=3mg$
(b) We know that the tension depends on $a_{cp}$ which is directly proportional to $v^2$ and inversely proportional to the radius $r$. As both $v^2$ and $r$ are proportional to l, therefore the length $l$ cancels out.
