The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are ${R}_{1}, {R}_{2}$ and ${H}_{1}$, ${H}_{2}$ respectively. Choose the correct option:

A particle is thrown with a velocity of $u \,m / s$. It passes $A$ and $B$ as shown in figure at time $t_1=1 \,s$ and $t_2=3 \,s$. The value of $u$ is ....... $m / s$ $\left(g=10 \,m / s ^2\right)$

A particle of mass $m$ is projected with velocity $v$ making an angle of ${45^o}$with the horizontal. The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is (where $g = $ acceleration due to gravity)

An object is projected from ground with speed $u$ at angle $\theta$ with horizontal. the radius of curvature of its trajectory at maximum height from ground is ..........

A particle is projected from the ground with an initial speed $\upsilon $ at an angle $\theta $ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

A ball of mass $m$ is thrown vertically upward. Another ball of mass $2\,m$ is thrown an angle $\theta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\frac{1}{x}$. The value of $x$ is $.....$