Question

A small block of mass of $0.1 \,kg$ lies on a fixed inclined plane PQ which makes an angle $\theta$ with the horizontal. A horizontal force of $1 N$ acts on the block through its centre of mass as shown in the figure. The block remains stationary if (take $g =10\, m / s ^{2}$ )

• 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 $Q$.

Answer 1

Answer: (A), (C)

At $\theta=45^{\circ}, mg \sin \theta=1 \times \cos \theta$
At $\theta>45^{\circ}, mg \sin \theta>1 \times \cos \theta$ (friction acts upward)
At $\theta<45^{\circ}, mg \sin \theta<1 \times \cos \theta$ (friction acts downward)