In the figure given below, a wooden block of mass \(2~\text{kg}\) rests on a soft horizontal floor. When an iron cylinder of mass \(25~\text{kg}\) is placed on top of the block, the floor yields steadily and the block and the cylinder together go down with an acceleration of \(0.1~\text{m/s}^{2}.\) What is the force of the block on the floor after the floor yields?
(take \(g=10~\text{m/s}^{2}\)${\mathrm{}}^{}$)
     
1. \(270~\text{N}\) upward
2. \(267.3~\text{N}\) downward
3. \(20~\text{N}\) downward
4. \(267.3~\text{N}\) 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.