A 2kg mass on a smooth inclined plane is connected over a smooth pulley to a 3kg mass. Find the acceleration of the system.

Let $m_1 = 2 \text{ kg}$ be the mass on the inclined plane.
Let $m_2 = 3 \text{ kg}$ be the hanging mass.
The angle of inclination is $\theta = 30^\circ$.
The plane is smooth, meaning there is no friction. The pulley is also smooth, meaning it is massless and frictionless.

For mass $m_2$ (hanging mass):
The forces are its weight $m_2 g$ acting downwards and the tension $T$ in the string acting upwards.
Since $m_2$ is heavier than $m_1$ (considering the component of $m_1$'s weight along the incline), $m_2$ will accelerate downwards.
Applying Newton's second law ($F_{net} = m_2 a$):

For mass $m_1$ (on the inclined plane):
The forces acting along the incline are the tension $T$ acting upwards along the incline and the component of its weight $m_1 g \sin\theta$ acting downwards along the incline.
Since $m_2$ accelerates downwards, $m_1$ will accelerate upwards along the incline.
Applying Newton's second law ($F_{net} = m_1 a$):

Add equation (1) and equation (2) to eliminate $T$:

Factor out $g$ on the left side and $a$ on the right side:

Solve for $a$:

We know that $\sin(30^\circ) = \frac{1}{2}$.

The final answer is $\frac{2g}{5}$.