## College Physics (4th Edition)

$\frac{T_1}{T_2} = \frac{m_1}{m_1+m_2}$
Let $a$ be the acceleration of the system. We can find an expression for the tension $T_1$: $T_1 = m_1~a$ We can find an expression for the tension $T_2$: $T_2 = (m_1+m_2)~a$ We can find an expression for the ratio $\frac{T_1}{T_2}$: $\frac{T_1}{T_2} = \frac{m_1~a}{(m_1+m_2)~a} = \frac{m_1}{m_1+m_2}$