Free body diagram
Case 1 -
When the system is at rest
Where F=upthrust
$F= T_0+mg$
Case 2 -
We know that when the $F'-T'-mg=ma$
We know that when a body is accelerated upwards with acceleration a. effective acceleration is $(g+a)$
$\therefore F'=F \bigg(\large\frac{g+a}{g}\bigg)$ --------(1)
$ F \bigg(\large\frac{g+a}{g}\bigg)$$-T=m (g+a) $ --------(2)
$(T_0+mg)\bigg(\large\frac{g+a}{g}\bigg)$$-m(g+a)=T^1$
$T_0 \bigg(\large\frac{g+a}{g}\bigg)$$+m(g+a)-m(g+a)=T^1$
$T'= T_0 \large\frac{(g+a)}{g}$
$\therefore $ Tension in the string increases
Hence a is the correct answer