Q: A block of mass m is to raised by a light rope from rest to rest through a height 60 m, the maximum tension of which the rope safely bear is 4 mg. The least time in which the ascent can be made is

(a) 1 s

(b) 2 s

(c) 3 s

(d) 4 s

Ans: (d)

Sol: Let up to t = t1 block is accelerated with maximum acceleration , then decelerated with deceleration g .

$ \displaystyle h_1 = \frac{1}{2}(\frac{4mg-mg}{m})t_1^2$

vo = 3gt1


0 = vo – g(t-t1)

t1 = t/4 ,

h2 = vo2/2g

h = h1 + h2

On solving

t= 4sec