Answer:
[tex]a = \frac{mg}{m + \frac{2}{5}M}[/tex]
Explanation:
To calculate the Acceleration and the tension of the object, we start by considering the value of the Tension through its moment of Inertia and Acceleration based on the angular velocity
[tex]\tau = I\alpha = Tension(T)*R[/tex]
And [tex]a = \alpha R[/tex]
Replacing,
[tex]T*R = I\alpha = (\frac{2}{5} MR^2)*\frac{a}{R})\\T*R = \frac{2}{5}MaR\\T = \frac{2}{5}Ma[/tex]
The following forces occur in the body,
[tex]mg - T = ma[/tex]
By this way we have the acceleration
[tex]mg - \frac{2}{5}Ma = ma[/tex]
[tex]a(m + \frac{2}{5})M) = mg[/tex]
[tex]a = \frac{mg}{m + \frac{2}{5}M}[/tex]
