With what minimum acceleration can a fireman slides down a rope while breaking strength of the rope is 23of his weight

If man slides down with some acceleration then its apparent weight decreases. For critical condition rope can bear only 2/3 of his weight. If a is the minimum acceleration then,Tension in the rope =m(g−a)=Breaking strength⇒m(g−a)=23mg⇒a=g−2g3=g3