Exercise $1$ : Size reduction

It is found that the power required to reduce particles from a mean diameter of $50\mathrm{.}8mm$ to $6\mathrm{.}35mm$ is $89\mathrm{.}5kW.$ Estimate the power requirement to reduce the same particles to $3\mathrm{.}18mm$ using:

$($a$)$ Rittinger's law.

$($b$)$ Kick's law.

$($c$)$ Bond's equation

Exercise $2$ : Size reduction

The power required to crush $125to\frac{n}{h}$ of unknown material is $100kW.$ Calculate the work index if $80\%$ of the feed passes a $2-$in screen and $80\%$ of the product passes a $\frac{1}{4}-$in screen.

Exercise $3$ : Size reduction

$150to\frac{n}{h}$ of gypsum rock is crushed in a certain crusher. The feed is nearly uniform $1\mathrm{.}50$ in spheres and produced the product of $0\mathrm{.}08$ in size. Using the Bond method, estimate the power necessary for the crushing process.