A frictionless circular wire of unit radius is fixed on the horizontal plane. Two-point particles of unit mass start moving simultaneously from point $A\left(\theta=\frac{\pi}{2}\right)$ with identical uniform angular speeds in opposite directions, and meet again at point $B\left(\theta=-\frac{\pi}{2}\right)$. During this time, which of the following figures schematically represent the magnitude of the total linear momentum $P$ of the system, as a function of $\theta$ ?

Two bodies $$A$$ and $$B$$ of same mass undergo completely inelastic one dimensional collision. The body $$A$$ moves with velocity $$v_1$$ while body $$B$$ is at rest before collision. The velocity of the system after collision is $$v_2$$. The ratio $$v_1: v_2$$ is

A bullet of mass $$m$$ hits a block of mass $$M$$ elastically. The transfer of energy is the maximum, when :