$A$ projectile is projected at an angle of $30^{\circ}$ from the horizontal with an initial velocity $u$. If the range of the projectile is $R$,what will be the range if the projectile is projected at an angle of $60^{\circ}$ with the same initial velocity?

The projectile motion of a particle of mass $5\, g$ is shown in the figure. The initial velocity of the particle is $5 \sqrt{2}\, m/s$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x \times 10^{-2}\, kg \cdot m/s$. The value of $x$,to the nearest integer,is ...... .

$A$ point $P$ on the circumference of a wheel is initially in contact with the ground. If the radius of the wheel is $5 \, m$,what will be the displacement of point $P$ when the wheel rolls forward by half a revolution?

$A$ projectile has the same range $R$ for two angles of projection. If $T_1$ and $T_2$ are the times of flight in the two cases,then $R$ is

List-$I$ describes four systems,each with two particles $A$ and $B$ in relative motion. List-$II$ gives possible magnitudes of their relative velocities (in $m s^{-1}$) at time $t = \frac{\pi}{3} s$. Which one of the following options is correct?

$A$ particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n u^2}{25 g}$,where the value of $n$ is (Given $g$ is the acceleration due to gravity).