$1$

A IC engine develops $250$ kW at $\backslash (90\backslash$mathrm$\{$r$\}.\backslash$mathrm$\{$p$\}.\backslash$mathrm$\{$m$\}\backslash ).$ The coefficient of fluctuation of energy as found from the turning moment diagram is to be $0\mathrm{.}2$ and the fluctuation of speed is to be kept within $\backslash (\backslash$pm $0\mathrm{.}3\backslash \%\backslash )$ of the mean speed. Find the mass of the flywheel required, if the radius of flywheel rim is $1\mathrm{.}5$ metres

$2$ The engine's flywheel has a mass of $6500$ kg $,$ and the radius of its rim is $1\mathrm{.}8$ meters. From the turning moment diagram, it is observed that the maximum fluctuation of energy is $56\backslash (\backslash$mathrm$\{$kN$\}\backslash$cdot $\backslash$mathrm$\{$m$\}\backslash ).$ The mean speed of the engine is given as $120$ RPM $.$ Calculate the maximum $(\backslash (\backslash$mathrm$\{$N$\}\_\{1\}\backslash ))$ and minimum $\backslash (\backslash$left$(\backslash$mathrm$\{$N$\}\_\{2\}\backslash$right$)\backslash )$ speeds of the flywheel.