a loadw is to b raised by a rope from rest to rest through a height h. the greatest tension the rope can safely bear is nw. th eleast time in which the ascent cabn b made will be

2 forces will act on the load:

1) tension upwards

2) mg downwards.

its to b pulled upwards in least time

so there must b an acceleration upwards.

let max tension be nw.

so, (nw)-mg=ma_max

a_max = (nw)-mg/m---------(1)

using equation s=ut+1/2at²

we get h= 0 + 1/2 {(nw) - mg/m}t²                                                (from 1)

           t^{2 =}  2mh/(nw)-mg

           t= √2mh/nw-mg