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(D) Since the block remains in a state of rest,for translational equilibrium:$F_x = 0 \implies F = N$$F_y = 0 \implies f = mg$For rotational equilibri

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$N$ will not produce torque

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(D) Since the block remains in a state of rest,for translational equilibrium:$F_x = 0 \implies F = N$$F_y = 0 \implies f = mg$For rotational equilibrium,the net torque $	au = 0$ about the center of mass $O$:$\vec{	au_F} + \vec{	au_f} + \vec{	au_N} + \vec{	au_{mg}} = 0$Since the lines of action of forces $F$ and $mg$ pass through the center of mass $O$,their torques about $O$ are zero.Thus,$\vec{	au_f} + \vec{	au_N} = 0$.Since the frictional force $f$ acts at the surface (distance $a$ from $O$),it produces a torque $\vec{	au_f} 
eq 0$. Therefore,$\vec{	au_N} 
eq 0$,meaning the normal reaction $N$ must also produce a torque to balance the torque produced by friction.

$A$ horizontal force $F$ is applied to a block as shown in the figure such that the block remains in a state of rest. Which of the following statements is true?

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