Don't wet the block

The specific gravity of the block $=$ $\frac{800}{1000}$ $=$ $0.8$ . Hence, the height inside water $=$ $3$ cm $\times$ $0.8$ $=$ $2.4$ cm and the height outside water $=$ $3$ cm $-$ $2.4$ cm $=$ $0.6$ cm

Suppose the maximum weight that can be put without wetting the block is $W$ . The block in this case is completely immersed in the water. The volume of the displaced water $=$ volume of the block $=$ $27 \times 10^{-6}$ $m^{3}$

Hence, the force of buoyancy $=$ $27 \times 10^{-6} \times 1000 \times 10$ $=$ $0.27$ N

The spring is compressed by $0.6$ cm and hence the upward force exerted by the spring $=$ $0.25 \times 0.6$ $=$ $0.15$ N.

The force of buoyancy and the spring force taken together balance the weight of the block plus the weight $W$ put on the block.

The weight of the block is $W_{b}$ $=$ $27 \times 10^{-6} \times 800 \times 10 = 0.216$ N $\approx$ $0.22$ N

Thus, $W$ $=$ $0.27$ N $+$ $0.15$ N $-$ $0.22$ N $=$ $\boxed{0.20}$ N