Step 1: Understand the condition for liberation of hydrogen gas.
A metal can liberate hydrogen gas from dilute hydrochloric acid only if it is more reactive than hydrogen. Metals placed above hydrogen in the activity series can displace hydrogen from acids, while metals placed below hydrogen cannot do so.
Step 2: Compare the given metals with hydrogen in the activity series.
Among the given metals, cobalt \(\mathrm{(Co)}\), nickel \(\mathrm{(Ni)}\), and zinc \(\mathrm{(Zn)}\) are above hydrogen in the reactivity series. Therefore, these metals react with hydrochloric acid and liberate hydrogen gas.
Copper \(\mathrm{(Cu)}\), however, lies below hydrogen in the activity series. Hence, it cannot displace hydrogen from dilute hydrochloric acid.
Step 3: Write the reasoning through reactions.
For reactive metals:
\[
\mathrm{Zn + 2HCl \rightarrow ZnCl_2 + H_2}
\]
Similarly, cobalt and nickel also react with HCl to release \(\mathrm{H_2}\). But copper does not show such a reaction with dilute HCl because it is less reactive than hydrogen.
Step 4: Conclusion.
Therefore, the metal which does not liberate hydrogen gas on reaction with hydrochloric acid is copper.
Final Answer:Cu.