GATE CS 2011 Q44 — I/O Scheduling

To find the total time required to load all $100$ libraries, we first calculate the average disk access time for a single random library access.

The total disk access time for one request is given by:

Let's calculate each component:

1. Seek Time: Given as $10\text{ ms}$.
2. Average Rotational Latency:
   The rotational speed of the disk is $6000\text{ rpm}$ (rotations per minute).
   Time for one full rotation = $\frac{60\text{ seconds}}{6000} = 0.01\text{ s} = 10\text{ ms}$.
   The average rotational latency is half of the time for one full rotation:$$\text{Average Rotational Latency} = \frac{10\text{ ms}}{2} = 5\text{ ms}$$
3. Transfer Time: Neglected as per the problem statement ($0\text{ ms}$).

Substituting these values into the access time formula:

Since the $100$ libraries are loaded from random locations, each library requires an independent random disk access. Therefore, the total time to load all $100$ libraries is:

Thus, the correct option is B.