A thin uniform equilateral plate rests in a vertical plane with one of its vertex $\mathrm{A}$ on a rough horizontal floor and another vertex $\mathrm{B}$ on a smooth vertical wall. If the coefficient of friction $\mu =\frac{1}{\sqrt{3}}$, then the least angle $\theta$ its base $\mathrm{AB}$ can make with the horizontal surface is

• A

  $\theta ={\cot }^{-1}\left[\mathrm{\mu }+\frac{1}{\sqrt{3}}\right]$
• B

  $\theta ={\tan }^{-1}\left[\mathrm{\mu }+\frac{1}{\sqrt{3}}\right]$
• C

  $\theta ={\tan }^{-1}\left[2\mathrm{\mu }+\frac{1}{\sqrt{3}}\right]$
• Correct answer
  D

  $\theta ={\cot }^{-1}\left[2\mathrm{\mu }+\frac{1}{\sqrt{3}}\right]$

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