A metal string A is suspended from a rigid support and its free end is attached to a block of mass M. Second block having mass 2 M is suspended at…

A metal string $\displaystyle A$ is suspended from a rigid support and its free end is attached to a block of mass $\displaystyle M$. Second block having mass $\displaystyle 2$ M is suspended at the bottom of the first block using a string $\displaystyle B$. The area of cross sections of strings $\displaystyle A$ and $\displaystyle B$ are same. The ratio of lengths of strings of $\displaystyle A$ to B is $\displaystyle 2$ and the ratio of their Young's moduli $\displaystyle \left(Y_A / Y_B\right)$ is $\displaystyle 0.5$ . The ratio of elongations in $\displaystyle A$ to $\displaystyle B$ is $\displaystyle \_\_\_\_$.