Answer
The mass needed to support the leg is 6.73kg.
Work Step by Step
We will sum the torque at the hip to find the mass, m;
$(+\circlearrowleft) \sum\tau=0$
$35cm*15kg*9.8m/s^2-m*9.8m/s^2*78cm=0$
$m=\frac{35cm*15kg*9.8m/s^2}{9.8m/s^2*78cm}$
$m\approx6.73kg$
Therefore, the mass needs to be 6.73kg