Bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length 10 m , as shown in the figure. Point mass $A$ of mass $m$ travelling horizontally with speed $10 \mathrm{~ms}^{-1}$ hits bob $B$ elastically. The bob $B$ rises $h$ meter after the collision. Taking the acceleration due to gravity $g=10 \mathrm{~ms}^{-2}$ and neglecting the size of the bob, the value of $h$ is:

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