mala06 said:
I have written the exact question and there is no wording about fixing the rope
Your image of the textbook "solution" certainly helped. Can you similarly supply an image of the problem statement from the textbook?
Lacking that at the moment ...
This is my take on this problem in light of the supplied "book" solution.
Both tension, T
1 and T
2 are arrived at assuming that the fiction forces are to the left, thus opposing motion to the right.
The value of T
1 that's calculated is the maximum value of tension, T, that will produce static equilibrium. (If we consider this to be a kinetic situation, then T
1 is the minimum value of tension, T, that will enable sustained motion to the right.)
T
2 is a bigger puzzle.
The value of T
2 that's calculated is the minimum value of tension, T, that will produce static equilibrium. Any smaller value for T
2 will give motion to the right. If T is greater than this (up to a point), then the static friction will simply be less than μ
2R
2, R being the normal force. (T
2 can be as large as 120.78 N for static equilibrium.)
Considering the values of T
1 and T
2, there is no possibility of this system being in static equilibrium.