Question

A Monkey of mass 20kg is holding a vertical rope. The Rope will not break when a mass of 25 kg is suspended from it but will break in the mass exceeds 25 kg .What is the maximum acceleration it with the monkey can climb up along the rope (G = 10 metre per second square)
My answer comes out to be 2.5m/s^2 but the answer is 25m/s^2 given in the book ....... How??

Answer 1

Let the monkey climb up with acceleration a. Then tension caused in the rope will be T =

M(g+a), where M is the mass of the monkey. Maximum value of T is 25g = 20(g + a). Taking

g = 10ms

-2, it gives a = 2.5 ms

Answer 2

The rope will not break unto 20kg it means it is its tension.

Thus balance condition

is  T-mg=ma

25g-20g= 20a    (g=10)     thus on solving a=50/20= 2.5m/s^ (ans)

So this  monkey can have max acceleration of2.5 if he really wants to climb the tree

Let the Monkey be climbing up with an acceleration 'a'.

Tension in string =m(g+a)

=Breaking force

20(g+a)=25×g

a=g4

=104

=2.5m/s2