### Video Transcript

Consider the physical
quantities π, π , π£, π, and π‘ with dimensions. Dimensions of π equals capital
π. Dimensions of π equals capital
πΏ. Dimensions of π£ equals πΏπ to
the negative one. Dimensions of π equals πΏ
times π to the negative two. And dimensions of π‘ equals
capital π. The equation π equals ππ
over π is dimensionally consistent. Find the dimension of the
quantity on the left-hand side of the equation.

We want to solve for the
dimension of the term capital π that appears on the left-hand side of the given
equation. Since weβre given an equation
that weβre told is dimensionally consistent, we can write that the dimensions of
π is equal to the dimension of π times the dimension of π divided by the
dimension of π. If we enter these dimensions
in. Where the dimension of π is
capital π. The dimension of π is capital
πΏ. And the dimension of π is πΏ
times π to the negative two. We see that, in this fraction,
the factors of length πΏ cancel out. And we can write it in a
simplified form as capital π times π squared. This is the net dimension of
the right-hand side of the equation. And since the equation is
dimensionally consistent, itβs also the dimension of capital π. So our result is capital π
times capital π squared.