A $2$ cm diameter steel ball $[$p$-7865$kg$/$m$^2,$ C$=0\mathrm{.}46$ kJ$/$kg$-$C and K $=61$ w$/$m$-$C$)$ is uniformly heated to $800\backslash$deg C$.$ It is to be hardened by suddenly droping it into an oil hath at $50\backslash$deg C$.$ It the quenching occurs when the ball reaches $100\backslash$deg C and the heat transfer co$-$efficient between the oil and the steel ball is $300$ w$/$m$^2$ C$,$ how long should the hall be kept in the oil hath?