A body of mass 2 kg is situated on a rough inclined plane of...

The force required to move the block up the rough inclined plane must overcome both the component of gravity along the incline and the maximum static friction.

The component of gravity parallel to the incline is:

$F_g = mg \sin \theta$

The normal force is:

$N = mg \cos \theta$

The maximum static friction force is:

$f_s = \mu_s N = \mu_s mg \cos \theta$

The total force $F$ required to move the block up the incline is:

$F = F_g + f_s = mg \sin \theta + \mu_s mg \cos \theta$

Substituting $m = 2 \text{ kg}$, \theta = 30^{}^{{}^{\circ}}, $\mu_s = 0.2$, and $g = 9.8 \text{ m/s}^2$:

F = 2 \times 9.8 \times \sin 30^{}^{{}^{\circ}} + 0.2 \times 2 \times 9.8 \times \cos 30^{}^{{}^{\circ}}

$F = 19.6 \times 0.5 + 3.92 \times \dfrac{\sqrt{3}}{2}$

$F = 9.8 + 1.96 \times 1.732$

$F = 9.8 + 3.39 = 13.19 \text{ N}$

The closest given option is $13 \text{ N}$.