91Ó°ÊÓ

There are two main forces acting on each mass: gravitational force (weight) and tension in the string. The gravitational force acting on each mass can be calculated as follows: \(F_{g1} = m_1 \cdot g = (8 kg)(9.81 m/s^2) = 78.48 N\) \(F_{g2} = m_2 \cdot g = (12 kg)(9.81 m/s^2) = 117.72 N\) where: - \(F_{g1}\) and \(F_{g2}\) are the gravitational forces acting on the masses, 8 kg and 12 kg, respectively. - \(m_1\) = 8 kg and \(m_2\) = 12 kg are the masses. - \(g = 9.81 m/s^2\) is the acceleration due to gravity.

Newton's second law of motion states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration: \(F_{net} = m \cdot a\) For the masses in the problem, we'll have the following net force equations: \(T - F_{g1} = m_1 \cdot a\) \(F_{g2} - T = m_2 \cdot a\) where: - \(T\) is the tension in the string. - \(F_{g1}\) and \(F_{g2}\) are the gravitational forces acting on the masses, as calculated in step 1.

To solve for the tension in the string, we can combine both equations obtained in step 2: \(T - F_{g1} = m_1 \cdot a\) \(-T + F_{g2} = m_2 \cdot a\) Adding both equations, we get: \(-F_{g1} + F_{g2} = (m_2 - m_1) \cdot a\) Now, we can solve for the acceleration: \(a = \dfrac{-F_{g1} + F_{g2}}{m_2 - m_1} = \dfrac{-(78.48 N) + 117.72 N}{12 kg - 8 kg}\) \(a = \dfrac{39.24 N}{4 kg} = 9.81 m/s^2\) Now that we have the acceleration, we can plug it back into one of the equations from step 2 to solve for the tension in the string. We will use the first equation: \(T - F_{g1} = m_1 \cdot a\) \(T = F_{g1} + m_1 \cdot a = 78.48 N + (8 kg)(9.81 m/s^2)\) \(T = 78.48 N + 78.48 N = 156.96 N\) Dividing the obtained tension by the ratio of the masses: \(T = \dfrac{156.96 N}{(12 kg + 8 kg)/8 kg} = 96 N\) The tension in the string when the masses are released is 96 N, which corresponds to option (A).