The correct option is A SN1 mechanism
The SN1 reaction proceeds stepwise. The leaving group first leaves, where upon a carbocation forms that is attacked by the nucleophile.
The SN2 occurs in one step. Both the nucleophile and substrate are involved in the rate determining step. Therefore, the rate is dependent on both the concentration of substrate and that of the nucleophile.
For tertiary butyl chloride, it forms tertiary carbocatin which is highly stable, So tertiary butyl chloride undergoes hydrolysis by SN1 mechanism. Hence, the correct option is (a).