\[\begin {array} {1 1} (a)\;\mu=\frac{1}{2} & \quad (b)\;\mu=\frac{1}{4} \\ (c)\;\mu=\frac{1}{3} & \quad (d)\;\mu=\frac{1}{5} \end {array}\]

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For translation equations :

$\sum F_x =0 => N_2= f_1$

$f_1=N_2$

$\sum F_y =0 => mg=f_2+N_1$

limiting equation

$f_1= \mu N_1$

$f_2= \mu N_2$

$f_1=N_2=\mu N_1$

$\therefore f_2=\mu ^2 N_1$

For rotational equation:

Taking torques about A:

Clock wise moments= Anti clock wise moments

$mg \times \frac{l}{2} \cos \theta+ f_1 \times l \sin \theta= N_1 \times l cos \theta$

Solving above equations:

$\mu =\large\frac{1}{3}$

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