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

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$

v_o = 3gt₁

Also

0 = v_o – g(t-t₁)

t₁ = t/4 ,

h₂ = v_o²/2g

h = h₁ + h₂

On solving

t= 4sec