First of all thank you so much for reading,
I was trying to solve the question below from "Concepts of Physics Vol1" by HC Verma.
What I was most interested in was the second part, "find the acceleration of the block and the pulley" This question was already solved in the book by firstly proving that if the pulley moved x the block moved 2x by some geometry, then by differentiating twice we got that the acceleration of A was twice the acceleration of B. But here is the interesting part written in the book.
It is given that the forces acting on the pulley are:-
"F towards right by experimenter,
T towards left by portion BC of the string,
T towards left by the portion BA of the string"
"As the mass of pulley is zero, the equation of motion is F-2T = 0, T = F/2".
And further we also calculated the acceleration of the pulley by
"Consider the block as the system. The only horizontal force acting on the block is the Tension T towards right. The acceleration of the block is a = T/m = F/2m. The acceleration of the pulley is a/2 (remember we got it by differentiating twice?) = F/4m."
But we know F = 2T, so the Net force on the pulley should be zero, then how is the pulley accelerating then, which we calculated, without any force in the inertial frame; even theoretically, considering it as massless?
