If force $=\frac{\alpha}{\text { density }+\beta^3}$, then the dimensional formulae of $\alpha$ and $\beta$ are respectively

• A

  $\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right],\left[\mathrm{M} \mathrm{L}^{-1 / 3} \mathrm{~T}^0\right]$
• B

  $\left[\mathrm{M}^2 \mathrm{~L}^4 \mathrm{~T}^{-2}\right],\left[\mathrm{M}^{1 / 3} \mathrm{~L}^{-1} \mathrm{~T}^0\right]$
• Correct answer
  C

  $\left[\mathrm{M}^2 \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right],\left[\mathrm{M}^{1 / 3} \mathrm{~L}^{-1} \mathrm{~T}^0\right]$
• D

  $\left[\mathrm{M}^2 \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right],\left[\mathrm{ML}^{-3} \mathrm{~T}^0\right]$

Hence, the correct answer is option: 'C'.