Can someone tell me the FBD and equations of body of mass m?

I have attached mine attempt (Did it in the frame of Block M).

M/m= coseca - 1?

No

M/m = (1-sina)^2/sina?

Write eqn of force for the block â€¦take effective accelerationâ€¦

yeah crct

1.) assume aâ€™ acceleration of M in left direction.

2.) write motion equations in frame of M

3.) write constraint relations(keep in mind we can directly use analogy for a here because alpha is a constant otherwise there is a possibility we have to use basics)

4.) for the mass m , resolve forces in directions perpendiduclar and parallel to the rope

5.) since alpha is constant we can equate summation of forces in perpendicular directions to be zero.

6.) you will get two unknowns aâ€™ and T.

7.) solve get your answer.

If you see carefully, i have done all this, yet i havenâ€™t got the answer. Please upload whole solution to it. The answer ainâ€™t matching the one provided in handout.

Why is effective acceleration g/cos(alpha)

Shitft the horizontal a vector downwards to form a triangleâ€¦check the direction of resultant vector â€¦

yeah this

Was this the most important step in this question to make the solution as simple as possible?

i didnâ€™t even understand the language of the question. I thought it meant it had fallen behind by 1.25 m