$A$ body is projected at an angle of $30^{\circ}$ with the horizontal with momentum $p$. At its highest point,the magnitude of the momentum is

$A$ bomb of mass $m$ is projected from the ground with speed $v$ at an angle $\theta$ with the horizontal. At the maximum height from the ground,it explodes into two fragments of equal mass. If one fragment comes to rest immediately after the explosion,then the horizontal range of the centre of mass is ..............

If $R$ and $H$ represent the horizontal range and the maximum height achieved by a projectile,then which of the following relations exists?

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$,but different maximum heights,$h_1$ and $h_2$. Which of the following is correct?

$A$ ball thrown by one player reaches another player in $2 \, s$. The maximum height attained by the ball is ........ $m$. (Take $g = 10 \, m/s^2$)

$A$ bob of mass $0.1\; kg$ hung from the ceiling of a room by a string $2\; m$ long is set into oscillation. The speed of the bob at its mean position is $1\; m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is
$(a)$ at one of its extreme positions,
$(b)$ at its mean position.