Rotating wheel on a V-groove

The axle of a wheel rests in a V-groove, as shown in figure, where

• a string fixed to the rim of the wheel holds a mass of $M,$
• $\mu = 0.5$ is the coefficient of friction between all the surfaces in contact,
• $W$ is the combined weight of the wheel and axle,
• $a$ is the radius of the axle,
• $b$ is the radius of the wheel, and
• $\theta$ is half the angle of the V-groove.

If the least value of $M$ which will cause motion is $\alpha \left( \frac{Wa}{g(5b\sin\theta - 2a)}\right)$ , then find the value of $\alpha$ .