(a) Volume of log of wood $V = \frac{mass}{density} = \frac{120}{600} = 0.2m^{3}$
Let $x$ weight that can be put on the log of wood
So weight of the body $= (120 + x) \times 10\ N$
Weight of displaced liquid $= V_{\sigma g} = 0.2 \times 10^{3} \times 10\ N$
The body will just sink in liquid if the weight of the body will be equal to the weight of displaced liquid
$\therefore(120 + x) \times 10 = 0.2 \times 10^{3} \times 10$
$\Rightarrow 120 + x = 200\ \therefore x = 80\ kg$