4 A ball \(B\) of mass 1.7 kg is connected to one end of a light elastic spring of natural length 1.2 m . The other end of the spring is attached to a point \(O\) on the ceiling of a large room. The modulus of elasticity of the spring is 50 N . The ball is held 3.2 m vertically below \(O\) and projected upwards with an initial speed of \(0.5 \mathrm {~ms} ^ { - 1 }\). In order to model the motion of \(B\) (before any collision with the ceiling) the following assumptions are made.

• Air resistance is ignored.
• \(B\) is small.
• The fully compressed length of the spring is negligible.
  1. Determine whether, according to the model, \(B\) reaches \(O\).
  2. Without doing any further calculations, explain whether the answer to part (i) could change in each of the following different cases.
     (a) A new model is used in which air resistance is taken into account.
     (b) The spring is replaced by an elastic string with the same natural length and modulus of elasticity.
     (c) \(\quad B\) is initially projected downwards rather than upwards.