Chapter 6, Problem 6.22HW

Program Plan Intro

Given Information:

A rotating disk in which number of bits per track is constant is given.

Explanation of Solution

Capacity of disk:

It is given that there is a rotating disk whose number of bits per track is constant. It is assumed that:

“r” denotes the radius of the platter and “$x\cdot r$” determines the radius of the hole.

• In a rotating disk, the number of bits per track will remain same which depends on the circumference of the innermost track.
• The most inner track can also be considered as a hole and the number of bits per track will increase if the hole is large and vice versa.

Hence, according to the given information:

“r” denotes the radius of the platter and “$x\cdot r$” determines the radius of

In a rotating disk, the radius of platter is greater than the radius of the hole which can be written as below:

$\begin{array}{l}r>x\cdot r\\ \Rightarrow x<r/r\\ \Rightarrow x<1\end{array}$

Hence, the value of x should be less than 1 in order to maximize the capacity of the disk and the value of x ranges from “$0<x<1$”.