Since the cube rise by 2cm there is a decrease in upthrust due to the decrease in weight.
Volume of water $=V=2 \times 10^{-2} \times Area\; of\; base$
upthrust $=V \rho _w g= 2 \times 10^{-2} \times A \times10^3 \times g$
$\therefore mg = 2 \times 10^{-2} \times A \times 10^3 \times g$
$0.2= 2 \times 10^{-2} \times 10^3 \times A$
$A=10^{-2}\;m^2$
$\therefore$ Side of the cube $=10\;cm$
Hence c is the correct answer.