We know that operating system is responsible for handling memory allocation, process management etc. CPU can perform only one task at a time(assuming it to be single core). Suppose an operating system has allocated a CPU cycle to some user initiated process and CPU is executing that. Now where is operating system running? If some other process is using the CPU, then, is operating system not running for that moment? as OS itself must need CPU to run. If in case OS is not running, then who is handling process management, device management etc for that period?
The question is mixing up who's in control of the memory and who's in control of the CPU. The wording “running” is imprecise: on a single CPU, a single task is running at any given time in the sense that the processor is executing its instructions; but many tasks are executing in the sense that their state is stored in memory and their execution can resume at any time.
While a process is executing on the CPU, the kernel is not executing. Its state is saved in memory. The execution of the kernel can resume:
- if the process code makes a jump into kernel code — this is called a system call.
- if an interrupt occurs.
If the operating system provides preemptive multitasking, it will schedule an interrupt to happen after an interval of time (called a time slice). On a non-preemptive operating system, the process will run forever if it doesn't yield the CPU. See How do modern operating systems like linux handle multitasking? for an explanation of how preemption works.
Tasks such as process management and device management are triggered by some event. If the event is a request by the process, the request will take the form of a system call, which executes kernel code. If the event is triggered from hardware, it will take the form of an interrupt, which executes kernel code.
(Note: in this answer, I use “CPU” and “processor” synonymously, to mean a single execution thread: a single core, or whatever the hardware architecture is.)
I think OP was asking whether the OS needs to run all the time on the CPU (to manage processes and other things). Therefore, I think the second answer fits best: The OS doesn't need to run all the time. Eventually it will run again due to the timer interrupt.
Your answer seems a bit more complicated because you're mostly referring to main memory (which OP didn't ask for imo).