$3($a$)$ A welding technician in a ship building company has to select a

suitable tool rotational speed $()$ to perform friction stir welding

process on Aluminium alloy with melting point $(T_m)660C.$ In order

to improve the production rate, the company has decided to use an

average welding speed $(v)$ of $90m\frac{m}{m}in.$ The exponential index $$

and proportionality constant $K$ are $0\mathrm{.}05$ and $0\mathrm{.}65,$ respectively. The

maximum temperature $(T)$ that can be obtained during friction stir

welding process is approximated as $0\mathrm{.}62T_m.$ Select the suitable

mathematical correlation from the following and estimate the

suitable tool rotational speed $().$

$\frac{T}{T_m}=K(\frac{{}^2}{v{10}^4}{)}^{}$

$\frac{T_m}{T}=K(\frac{v}{{}^2{10}^4}{)}^{}$