In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $\mathrm{\theta }$ with the horizontal floor. The coefficient of friction between the wall and the ladder is ${\mathrm{\mu }}_1$ and that between the floor and the ladder is ${\mathrm{\mu }}_2$ . The normal reaction of the wall on the ladder is ${\mathrm{N}}_1$ and that of the floor is ${\mathrm{N}}_2$ If the ladder is about to slip, then

• A

  ${\mathrm{\mu }}_1=0\mathrm{ }{\mathrm{\mu }}_2\ne 0$ and ${\mathrm{N}}_2\tan \mathrm{\theta }=\frac{\mathrm{m}\mathrm{g}}{2}$
• B

  ${\mathrm{\mu }}_1\ne 0\mathrm{ }{\mathrm{\mu }}_2=0$ and ${\mathrm{N}}_1\tan \mathrm{\theta }=\frac{\mathrm{m}\mathrm{g}}{2}$
• Correct answer
  C

  ${\mathrm{\mu }}_1\ne 0\mathrm{ }{\mathrm{\mu }}_2\ne 0$ and ${\mathrm{N}}_2=\frac{\mathrm{m}\mathrm{g}}{1+{\mathrm{\mu }}_1{\mathrm{\mu }}_2}$
• Correct answer
  D

  ${\mathrm{\mu }}_1=0\mathrm{ }{\mathrm{\mu }}_1\ne 0$ and ${\mathrm{N}}_1\tan \mathrm{\theta }=\frac{\mathrm{m}\mathrm{g}}{2}$

Hence, the correct answer is options: 'C', 'D'.