A particle of mass \(m\) is moving in \(yz\text-\)plane with a uniform velocity \(v\) with its trajectory running parallel to the \(+\text{ve}\) \(y\text{-}\)axis and intersecting \(z\text{-}\)axis at \(z=a\) in the figure. The change in its angular momentum about the origin as it bounces elastically from a wall at \(y\) = constant is:

         
1. \(mva~\hat e_{x}\)
2. \(2mva~\hat e_{x}\)
3. \(ymva~\hat e_{x}\)
4. \(2ymva~\hat e_{x}\)

A merry-go-round, made of a ring-like platform of radius \(R\) and mass \(M,\) is revolving with the angular speed $\mathrm{\omega }$. A person of mass \(M\) is standing on its edge. At one instant, the person jumps off the round such that the final speed of the person is zero. What is the final angular velocity of the merry-go-round?
1. \(2\omega\)
2. \(\omega\)
3. \(\omega/2\)
4. \(0\)
$\begin{array}{l}\end{array}$

The figure below shows two identical particles 1 and 2, each of mass \(m,\) moving in opposite directions with the same speed \(v\) along parallel lines. At a particular instant, \(r_1\) and \(r_2\) are their respective position vectors drawn from point A, which is in the plane of the parallel lines.

      
Consider the following statements.

Choose the correct option: