# A Monkey of mass m climbs up to a rope hung over a fixed pulley with acceleration g/4. The opposite end of the rope is tied to a block of mass M lying on a rough horizontal plane. The coefficient of friction between the block and horizontal plane is μ. Find the tension in the rope.

Salim Shamim
37 Points
11 years ago

As monkey is accelerating upwards by g/4 it must be applying its mass times its acceleration force downwards.

THUS

Force ON ROPE

by monkey :- m*(g/4) downwards + its mass times acceleration due to gravity     i.e m*g

Fnet=m(g+g/4)= 5mg/4 which equals the tension.

till Fnet≤µMg

Utkarsh Verma
33 Points
11 years ago

I tried this question and was able to solve!

Acceleration of Monkey/Rope = g/4

Let the acceleration of ''M'' = a

So, the acceleration of the rope = a

(a)monkey = (a)monkey/rope + (a)rope

= (a-g/4)

For mass M, T - μmg = Ma                        ...(1)

For Monkey, mg - T = m(a - g/4)              ...(2)

From equation (1) and (2),

mg - μMg = a(M + m) - mg/4

Then,

a = (5m/4 - μM)g / (M + m) = (5m - 4μM)g / 4(M + m)

Therefore, T = [M(5m - 4μM)g / 4(M + m)] - μMg