Two masses M_1 and M_2 are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M_2 is…

Two masses $\displaystyle M_1$ and $\displaystyle M_2$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $\displaystyle M_2$ is twice that of $\displaystyle M_1$, the acceleration of the system is $\displaystyle a_1$. When the mass $\displaystyle M_2$ is thrice that of $\displaystyle M_1$, the acceleration of the system is $\displaystyle a_2$. The ratio $\displaystyle \frac{a_1}{a_2}$ will be :