A solid disc of radius $$a$$ and mass $$m$$ rolls down without slipping on an inclined plane making an angle $$\theta$$ with the horizontal. The acceleration of the disc will be $$\frac{2}{b}g\sin\theta$$, where $$b$$ is ________. (Round off to the Nearest Integer) ($$g$$ = acceleration due to gravity, $$\theta$$ = angle as shown in figure)

For a solid disc rolling without slipping on an inclined plane, the acceleration is given by $$a = \frac{g\sin\theta}{1 + \frac{I}{mR^2}}$$.

The moment of inertia of a solid disc about its center is $$I = \frac{1}{2}ma^2$$, where $$a$$ is the radius. So $$\frac{I}{ma^2} = \frac{1}{2}$$.

Therefore, $$a = \frac{g\sin\theta}{1 + \frac{1}{2}} = \frac{g\sin\theta}{\frac{3}{2}} = \frac{2}{3}g\sin\theta$$.

Comparing with the given expression $$\frac{2}{b}g\sin\theta$$, we get $$b = 3$$.

The value of $$b$$ is $$\boxed{3}$$.