Disk capacity

Question

Assume innermost track has diameter 1 cm and outermost track has diameter 10 cm. There are 10 tracks in the disk and it is rotating with constant linear velocity. Capacity of innermost track is 1MB. Total capacity of the disk is ____ ?

Answer 1

We know that the transfer time means the amount of data to be transferred in 1 rotation time and this is the data taken equivalent to a particular track..Now say the radius of inner track = r₁  and radius of outer track = r₂ , angular velocity of inner track = ω₁ and angular velocity of outer track = ω₂ ..As linear velocity of tracks is given to be constant ,

ω₁r₁  =  ω₂r₂

So outer tracks having more radius will have less angular velocity .Hence less angular velocity means less no of rotations per unit time means more time required for 1 rotation..So more amount of data will be transmitted assuming transfer rate of data is constant..So more data is transferred if we have more radius .So capacity of outer track will be more..

So it will be proportional to radius of track..

Given capacity of innermost track = 1 MB

So  capacity of 2nd innermost track = 2 MB

capacity of 3rd innermost track = 3 MB

and so on till the outermost track which has 10 MB capcacity..

So total capacity of disk  =  1 + 2 + 3 .........10

                                     =   55 MB

Had the constraint been given "constant angular velocity" then in that case same rotational time of each track so same capacity would be there..In that case,

Total capacity of disk   =  10 MB

Comments

Habib, But I have read somewhere Capacity of Tracks remains Same.   Density decreases outwards.

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Actually similar question came in gate-2005it..The link is :

https://gateoverflow.in/3845/gate2005-it_81a

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@Habib I agree with @mcjoshi

Capacity of disk is fixed

But transfer speed can be changed