In the figure given below, a wooden block of mass \(2\) kg rests on a soft horizontal floor. When an iron cylinder of mass \(25\) kg is placed on top of the block, the floor yields steadily and the block and the cylinder together go down with an acceleration of \(0.1~\mathrm{m/s^2}\). What is the force of the block on the floor after the floor yields? (Take \(g=10~\mathrm{m/s^2}\)${\mathrm{}}^{}$.)

1. \(270\) N upward
2. \(267.3\) N downward
3. \(20\) N downward
4. \(267.3\) N upward

Conservation of momentum in a collision between particles can be understood from:

See the figure given below. A mass of \(6\) kg is suspended by a rope of length \(2\) m from the ceiling. A force of \(50\) N is applied at the mid-point \(P\) of the rope in the horizontal direction, as shown. What angle does the rope make with the vertical in equilibrium? (Take \(g=10~\text{ms}^{-2}\)). Neglect the mass of the rope.