Physics - Unit & Dimension Question with Solution | TestHub

Given: $F=a{x}^2+b{t}^{\frac{1}{2}}$

Dimension of $\left[a\right]=\frac{\left[F\right]}{\left[x^2\right]}=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}=\left[M^1{L}^{-1}{T}^{-2}\right]$

Dimension of $\left[b\right]=\frac{\left[F\right]}{\left[t^{{\displaystyle \frac{1}{2}}}\right]}=\frac{\left[ML{T}^{-2}\right]}{\left[T^{{\displaystyle \frac{1}{2}}}\right]}=\left[M^1{L}^1{T}^{-\frac{5}{2}}\right]$

Required value, $\left[\frac{b^2}{a}\right]=\frac{\left[M^2{L}^2{T}^{-5}\right]}{\left[M^1{L}^{-1}{T}^{-2}\right]}=\left[M^1{L}^3{T}^{-3}\right]$