Linear Density, $m$ has dimensions of $\frac{\text { Mass }}{\text { Length }}= ML ^{-1}$ and Force, $A$, has dimensions $MLT ^{-2}$

Thus dimensions of $B$ are $\frac{ MLT ^{-2}}{ ML ^{-1}}= L ^2 T ^{-2}$, which is the same as Latent Heat (which is heat per unit mass, or $\frac{ ML ^2 T ^{-2}}{ M }= L ^2 T ^{-2}$ )