In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $$\theta$$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $$\mu$$₁ and that between the floor and the ladder is $$\mu$$₂. The normal reaction of the wall on the ladder is N₁ and that of the floor is N₂. If the ladder is about to slip, then

A small block of mass 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/s²)

A reference frame attached to the earth

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit $$ - \phi $$ and $$ + \phi $$. For an angular displacement $$\theta $$ $$\left( {\left| \theta \right| < \phi } \right)$$, the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions: