The dimensionless ratio of inertial force to surface tension torce, weber number and is expressed bubbic formation and the break$-$un of jets of liquids, is called the Weber nuber and is as: $W_f=\frac{u^{2}L}{g},$ where $u$ is the velocity, $$ is the density, $L$ is a characteristic length and $$ is the surface tension of the liquid $($with S$.$I. units of $\frac{N}{m}).$ Use the dimensions of these quantities to find the dimensions of $g_C.$

Ans. $,g_c$ is dimensionless.