$A$ body $P$ is projected at an angle of $30^{\circ}$ with the horizontal and another body $Q$ is projected at an angle of $30^{\circ}$ with the vertical. If the ratio of the horizontal ranges of the bodies $P$ and $Q$ is $1: 2$,then the ratio of the maximum heights reached by the bodies $P$ and $Q$ is

Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal force is

The coordinates of a particle moving in a plane are given by $x = a \cos(pt)$ and $y = b \sin(pt)$,where $a, b (b < a)$ and $p$ are positive constants of appropriate dimensions. Then:

$A$ particle moving in the $xy$ plane experiences a velocity-dependent force $\overrightarrow{F} = k(v_y \hat{i} + v_x \hat{j})$,where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\overrightarrow{v}$. If $\overrightarrow{a}$ is the acceleration of the particle,then which of the following statements is true for the particle?

Column-$I$ (Angle of projection)	Column-$II$
$A. \theta = 45^{\circ}$	$1. \frac{K_h}{K_i} = \frac{1}{4}$
$B. \theta = 60^{\circ}$	$2. \frac{gT^2}{R} = 8$
$C. \theta = 30^{\circ}$	$3. \frac{R}{H} = 4\sqrt{3}$
$D. \theta = \tan^{-1}(4)$	$4. \frac{R}{H} = 4$

$K_i:$ initial kinetic energy,$K_h:$ kinetic energy at the highest point.

$A$ charged particle of mass $m = 2 \ kg$ and charge $q = 1 \ \mu C$ is projected from a horizontal ground at an angle $\theta = 45^{\circ}$ with speed $u = 10 \ ms^{-1}$. In space,a horizontal electric field $E = 2 \times 10^7 \ NC^{-1}$ exists in the direction of projection. The range of the projectile is......$m$.