Three blocks of masses \(m_1\), \(m_2\), and \(m_3\) are connected in series on a rough horizontal table by two taut, light cords: Cord 1 connects Block 1 to Block 2, and Cord 2 connects Block 2 to Block 3.

A constant horizontal pulling force of magnitude \(F\) is applied to Block 3 to the right, causing the entire assembly to accelerate across the table, where the coefficient of kinetic friction between each block and the table is a uniform value \(\mu\).

A student analyzes the assembly to determine the tension \(T_2\) in Cord 2.

Which of the following correctly gives \(T_2\) in terms of the given quantities, and explains why analyzing the two-block subsystem of Blocks 1 and 2 allows \(T_2\) to be determined without calculating the tension \(T_1\) in Cord 1?