A piece of ice (heat capacity =2100 ~J ~kg^ -1 ^ C^ -1 and latent...

Language of question is slightly wrong. As heat capacity and specific heat are two different physical quantities. Unit $\mathrm{J}-\mathrm{kg}^{-1} \cdot{ }^{{}^{\circ}} \mathrm{C}^{-1}$. The heat capacity given in the question is really the specific heat. Now applying the heat exchange equation. $$\begin{array}{r}420=\left(m \times10^{-3}\right)(2100)(5)+\left(1 \times10^{-3}\right) \\ \left(3.36 \times10^5\right) \end{array}$$ Solving this equation we get, m=8 \mathrm{~g}\therefore The correct answer is 8 .