Step 1: Understanding the Concept:
The question describes a scenario of obtaining property through threats and asks to identify the specific offence under the IPC. This requires a careful analysis of the elements of extortion and robbery.
Step 2: Detailed Explanation:
\begin{itemize}
\item Extortion (Section 383 IPC): The essential ingredients of extortion are:
\begin{enumerate}
\item Intentionally putting a person in fear of any injury (to themselves or another).
\item Dishonestly inducing the person so put in fear to deliver any property or valuable security.
\end{enumerate}
In the given scenario, A puts Z in fear of injury (death) to Z's child and thereby dishonestly induces Z to deliver property (Rs. 10,000). All the elements of extortion are met.
\item Robbery (Section 390 IPC): Robbery is an aggravated form of either theft or extortion. For extortion to become robbery, the offender must, at the time of committing the extortion, be in the presence of the person put in fear, and commit the extortion by putting that person in fear of instant death, instant hurt, or instant wrongful restraint.
In this case, the threat is of future harm ("will be put to death") and there is no indication that A is in the presence of Z when making the threat and receiving the money. The element of "instant" fear and "presence" is missing. Therefore, it is not robbery.
\item Dacoity (Section 391 IPC): Dacoity is robbery committed by five or more persons. Since the offence is not robbery, it cannot be dacoity.
\end{itemize}
Step 3: Final Answer:
The offence committed is Extortion.