A small block of mass of $0.1 \ kg$ lies on a fixed inclined plane $P Q$ which makes an angle $\theta$ with the horizontal. A horizontal force of $1 \ N$ on the block through its center of mass as shown in the figure. The block remains stationary if (take $g =10 \ m / s ^2$ ) $Image$
$(A)$ $\theta=45^{\circ}$
$(B)$ $\theta>45^{\circ}$ and a frictional force acts on the block towards $P$.
$(C)$ $\theta>45^{\circ}$ and a frictional force acts on the block towards $Q$.
$(D)$ $\theta<45^{\circ}$ and a frictional force acts on the block towards $Q$.
IIT 2012, Difficult
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$f =0$, If $\sin \theta=\cos \theta \quad \Rightarrow \quad \theta=45^{\circ}$
f towards $Q, \sin \theta>\cos \theta \Rightarrow \quad \theta>45^{\circ}$
f towards $P, \sin \theta<\cos \theta \Rightarrow \quad \theta<45^{\circ}$
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