# GATE - 2005 | OS | A disk has 8 equidistant tracks.

## Question:

A disk has 8 equidistant tracks. The diameters of the innermost and outermost tracks are 1 cm and 8 cm respectively. The innermost track has a storage capacity of 10 MB. If the disk has 20 sectors per track and is currently at the end of the 5th sector of the inner-most track and the head can move at a speed of 10 meters/sec and it is rotating at constant angular velocity of 6000 RPM, how much time will it take to read 1 MB contiguous data starting from the sector 4 of the outer-most track?

 A 13.5 ms B 10 ms C 9.5 ms D 20 ms

## Solution:

### Option (A) is Correct.

Radius of inner track is 0.5cm (where the head is standing) and the radius of outermost track is 4cm.

So, the header has to seek (4 - 0.5) = 3.5cm.
For 10m ------- 1s
1m ------- 1/10 s
100cm ------- 1/(10×100) s
3.5cm ------- 3.5/1000 s = 3.5ms
So, the header will take 3.5ms.

Now, angulur velocity is constant and header is now at end of 5th sector. To start from front of 4th sector it must rotate upto 18 sector.

6000 rotation in 60000ms.
1 rotation in 10ms (time to traverse 20 sectors).
So, to traverse 18 sectors, it takes 9ms.
In 10ms, 10MB data is read.

So, 1MB data can be read in 1ms.

∴ Total time = 1+9+3.5 = 13.5ms

Thank You