A block of mass \( M=4 \mathrm{~kg} \) of height \( h^{\prime} \) and breath \( b \) is placed o...

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A block of mass \( M=4 \mathrm{~kg} \) of height \( h^{\prime} \) and breath \( b \) is placed on a rough plank of same mass \( M \). A light inextensible string is connected to the upper end of the block and passed through a light smooth pulley as shown in figure. A mass \( m=1 \mathrm{~kg} \) is hung to the other end of the string.

What should be the minimum value of coefficient of friction between the block and the plank so that, there is no slipping between the block and the wedge?
(1) \( \frac{3}{5} \)
(2) \( \frac{5}{9} \)
(3) \( \frac{4}{5} \)
(4) \( \frac{1}{9} \)
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