Question

Energy (E) [M] [L] ^{2 /[T] 2}

Distance (x) =[L]

Here [L] ` [T] and [M] denote respectively dimensions of length, time and mass

Now consider the equation. E=1/2 kx²

What must be the dimensions of k in order for the equation to be dimentally correct

Answer 1

Express k in terms of other quantities:

$$k=\frac{2E}{x^2},\\\space\\ k=\frac{[M] [L] ^2 [T] ^{-2}}{[L]^2}=[M][T]^{-2}.$$