Constraint equations in mechanics

[Kushal Chakrabarti]

1. The problem: Two blocks of mass m=5kg and M= 10kg are connected by a string passing over a pulley B. Another string connects pulley B to the floor and passes over pulley A. An upward force F is applied at the centre of pulley A. Both pulleys are massless. Find acceleration of the blocks if F is:
a) 100N, b) 300N, c) 500N
Take g=10 ms^-2
I have attached an image of the problem.

Attempt at a solution:
Well I drew an FBD in the frame of pulley A, thus using a downward pseudo force. Also, I found using constraint equations that F=4T, where T is the tension in the thread joining the two masses. Thus it gave me two equations ( one for each mass) but solving them, I found out that both the accelerations are turning out to be negative. Where did I go wrong?

 

[Orodruin]

Thus it gave me two equations ( one for each mass) but solving them, I found out that both the accelerations are turning out to be negative. Where did I go wrong?

How are we going to have any chance to answer that if you do not show us your calculations?

 

[Kushal Chakrabarti]

How are we going to have any chance to answer that if you do not show us your calculations?

I'm very sorry sir I'll put my attempt too

 

[Kushal Chakrabarti]

 

[Kushal Chakrabarti]

How are we going to have any chance to answer that if you do not show us your calculations?

I've now added my attempt too, sir

 

[haruspex]

View attachment 228172

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The line F=(M+m)a omits that a cord is anchored to the floor. It is also wrong in supposing that the mass centre of the two masses accelerates at the same rate as the upper pulley.