question_answer

Identify the physical quantity x defined as  \[x=\frac{IF{{\upsilon }^{2}}}{W{{l}^{3}}}\], where I is moment of inertia, F is force, \[\upsilon \]is velocity, W is work and l is length.

Answer:

                As       \[I=\left[ M{{L}^{2}} \right]\], \[F=\left[ ML{{T}^{-2}} \right]\], \[\upsilon =\left[ L{{T}^{-1}} \right]\]and \[W=\left[ M{{L}^{2}}{{T}^{-2}} \right]\]                 \[\therefore \] \[x=\frac{IF{{\upsilon }^{2}}}{W{{l}^{3}}}=\frac{\left[ M{{L}^{2}} \right]\left[ ML{{T}^{-2}} \right]{{\left[ L{{T}^{-1}} \right]}^{2}}}{\left[ M{{L}^{2}}{{T}^{-2}} \right]\left[ {{L}^{3}} \right]}=\left[ M{{L}^{0}}{{T}^{-2}} \right]\] These are the dimensions of surface tension; force constant, energy/area.