Mass and pulley system question


A mass M = 53 g hangs from a light, inextensible string. It passes without sliding over a pulley. The pulley can be treated as a solid homogeneous disc with mass mp = 12 g and radius 3.6 cm, that turns without friction on its axis. The other end is attached to a mass m = 27 g that slides without friction on a plane inclined at angle θ = 25° to the horizontal. What is the acceleration of mass M?

2. Relevant equations

I of disk = 1/2MR^2

3. The attempt at a solution

Okay, so I am attempting to find the acceleration of the mass downwards. Due to Newton’s second law, the sum of all forces is 0. Therefore logically, the acceleration should be

acceleration of M = Mg – (inertia of disk + mgsin(x) )

so acceleration of M = 0.054×9.8 – [(0.5 x 0.012 x 3.6^2) + (0.027x 9.8 x sin25)]

But for some reason I am not getting the right answer. Am I approaching it incorrectly?

Attached Images
File Type: jpg mass problem.JPG (11.8 KB)

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