Answer
(a) Please see the work below.
(b) $\frac{1}{3}$
Work Step by Step
(a) We know that if the fraction of the tie hanging from the table is increased, the force of gravity on that part increases and it will be greater than the force of static friction acting on that part of the tie. Thus, the tie slowly slides down.
(b) We can find the required coefficient of static friction as follows:
$f_s=\mu_s N$
$\implies \frac{1}{4}mg=\mu_sN$
$\implies \frac{1}{4}mg=\mu_s(\frac{3}{4}m)g$
This simplifies to:
$\mu_s=\frac{1}{3}$
