$A$ uniform chain has a mass $m$ and length $l$. It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done in just pulling the hanging part back on the table is

Liquids $A$ and $B$ form ideal solution over the entire range of composition. At temperature $T$, equimolar binary solution of liquids $A$ and $B$ has vapour pressure $45$ Torr. At the same temperature, a new solution of $A$ and $B$ having mole fractions $x_A$ and $x_B$, respectively, has vapour pressure of $22.5$ Torr. The value of $x_A / x_B$ in the new solution is. . . . . (given that the vapour pressure of pure liquid $A$ is $20$ Torr at temperature $T$ )