A small block of mass of $0.1 \mathrm{~kg}$ lies on a fixed inclined plane PQ which makes an angle $\theta$…

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

1. $\theta=45^{\circ}$
2. $\theta>45^{\circ}$ and a frictional force acts on the block towards P.
3. $\theta>45^{\circ}$ and a frictional force acts on the block towards Q.
4. $\theta < 45^{\circ}$ and a frictional force acts on the block towards Q.

Solution

The various forces acting on the block are as shown in the figure.
When $\theta=45^{\circ}, \sin \theta=\cos \theta$ The block will remain stationary and the frictional force is zero. When $\theta>45^{\circ}, \sin \theta>\cos \theta$ Therefore a frictional force acts towards $Q$. When $\theta < 45^{\circ}, \cos \theta>\sin \theta$ Therefore a frictional force acts towards $P$. `

Asked in: JEE Advanced 2012 (Paper 1)

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