In order to raise a mass of 100 kg a man of mass 60 kg fastens a rope to it and passes the Rope over a smooth Pulley. He climbs the rope with an acceleration 5g/4 relative to rope .the tension in the Rope is. g is acceleration due to gravity . Take g=10

The smaller mass is accelerated upwards which in turn lifts the the heavier mass upward at some rate as well. The heavier mass is accelerating with 'a' while the smaller mass is accelerating with 'am', while 'ar' is the relative acceleration of smaller mass.

Here we shall establish the two equations of motion using the above diagram

T – mg = mam………….(a)

 T – Mg = Ma…………(b)

Now we shall calculate the value of acceleration 'a' by equating equations (a) and (b).

so,

Mg – mg = Ma - mam

however, we know that

 am =  ar  - a

so, the above relation becomes

g(M-m) = Ma - m.ar + ma

g(M-m) +  m.ar = a(M+m)

a = [g(M-m) +  m.ar]/(M+m)

now, here

M = 100 kg

m = 60 kg

ar = (5/4)g

so,

a =  (-400 + 750)/160

or acceleration

a  =  35/16 m/s2 = 2.1875 m/s2

now, the tension will be calculated as, using equation (b)

T = M(g+ 2.1875)

 = 100 x 12.1875

i.e. T  = 1218.75 N