Step 1: Understanding the reaction of metals with dilute acids.
Metals that are placed above hydrogen in the reactivity series can displace hydrogen from dilute acids such as dilute sulphuric acid. These metals react with dilute \( \mathrm{H_2SO_4} \) to form metal sulphates along with the evolution of hydrogen gas.
Step 2: Analyzing each option.
(A) Fe: Iron is above hydrogen in the reactivity series. Therefore, it reacts with dilute sulphuric acid to form ferrous sulphate and hydrogen gas. Hence, this option is correct.
(B) Bi: Bismuth is less reactive and lies below hydrogen in the reactivity series. It does not react with dilute sulphuric acid.
(C) Cu: Copper is a less reactive metal and is placed below hydrogen. It does not displace hydrogen from dilute sulphuric acid.
(D) Hg: Mercury is also below hydrogen in the reactivity series and does not react with dilute sulphuric acid.
Step 3: Conclusion.
Only iron can react with dilute sulphuric acid among the given metals because it is more reactive than hydrogen.