To solve this problem, we need to find the acceleration of the system using Newton's second law.$\\$Consider the two masses:$\\$• Mass $m_1 = 4$ kg (on the left)$\\$• Mass $m_2 = 6$ kg (on the right)$\\$The forces acting on the masses are due to gravity:$\\$• Force on $m_1: F_1 = m_1 \cdot g = 4g \\$• Force on $m_2: F_2 = m_2 \cdot g = 6g \\$Since the pulley is frictionless and the string is massless, the tension $T$ is the same on both sides.$\\$For $m_1$ (4 kg mass), applying Newton's second law:$\\ T - 4g = 4a \quad (1) \\$For $m_2$ (6 kg mass), applying Newton's second law:$\\ 6g - T = 6a \quad (2) \\$Add equations (1) and (2) to eliminate $T: \\ (T - 4g) + (6g - T) = 4a + 6a \\ 2g = 10a \\ a = \frac{g}{5} \\$Therefore, the acceleration of the system is $\frac{g}{5}. \\$This corresponds to Option 2.