\[\begin {array} {1 1} (a)\;1 & \quad (b)\;\frac{9}{10} \\ (c)\;\frac{10}{9} & \quad (d)\;none\;of\;these \end {array}\]

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Sphere in (a) is in transnational equilibrium. Sphere in (a)

$ \sum F_Y=0$

$mg= f_1+N_2$

$ \sum F_X=0$

$f_2=N_1$

$f_1=\mu N_1$

$f_2= \mu N_2$

$\mu N_2 =N_1$

$N_2=\large\frac{N_1}{\mu}$

$\therefore mg =\large\frac{N_1}{\mu}$$+\mu N_1$

$ \large\frac{\mu mg}{\mu^2+1}$$=N_1$

$N_2= \large\frac{mg}{\mu^2 +1}$

$f_a= \large\frac{\mu mg}{\mu^2+1}$

$\qquad= \large\frac{3mg}{10}$

For sphere in (b)

Since $f_2$ is acting toward right, the sphere has a tendency to move towards right.

$N_1=0, f_1=0$

$\therefore mg=N_2$

$f_2 = \mu mg=\large\frac{mg}{3}$

$\therefore \large\frac{f_a}{f_b}=\frac{9}{10}$

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