Key idea: variation of molar conductivity with concentration
Molar conductivity, $\Lambda_m$, generally increases on dilution (i.e. decreases with increase in concentration).

How strong and weak electrolytes differ

• For a strong electrolyte (like HCl, NaCl, $KNO_3$), the plot of $\Lambda_m$ vs $\sqrt{c}$ is nearly linear, and with concentration it changes gradually.
• For a weak electrolyte (like $CH_3COOH$), molar conductivity changes very sharply on dilution, because degree of ionization increases strongly as concentration decreases.

Interpretation of the given graph
Since the graph corresponds to a variation characteristic of a weak electrolyte, electrolyte $X$ must be a weak electrolyte.

Check the options

• A: HCl → strong electrolyte
• B: $CH_3COOH$ → weak electrolyte
• C: NaCl → strong electrolyte
• D: $KNO_3$ → strong electrolyte

Conclusion
Therefore, the electrolyte is: $\boxed{CH_3COOH}$ which is Option B.