$3\mathrm{.}2.($b$)$ A $200kW$ mill is treating $50$ tons of ore per hour and the feed and product size distributions

are as shown in the graph below:

You are told that the mill runs at $75\%$ of critical speed and at a mill filling $J$ of $30\%.$

You are also told that the mill diameter is equal to the mill length.

From the provided information solve the following:

$($i$)$ Estimate the work index of this ore $(8)$

$($ii$)$ Calculate the diameter of this mill $(10)$

$($iii$)$ The mill is now replaced by another that is geometrically similar but $10\%$ bigger.

What will be the product size if the ore feed rate and all the operation parameters remain the

same $(12).$