$A$ body of mass $100 \, g$ is projected at an angle of $30^\circ$ with the horizontal with a velocity of $20 \, m \, s^{-1}$. What is the change in its momentum at the maximum height in $kg \, m \, s^{-1}$?

Three point particles $P, Q, R$ move in a circle of radius $r$ with different but constant speeds. They start moving at $t = 0$ from their initial positions as shown in the figure. The angular velocities (in $\text{rad/s}$) of $P, Q$ and $R$ are $5\pi, 2\pi$ and $3\pi$ respectively,in the same sense. The number of times $P$ and $Q$ meet in the time interval $t = 0$ to $t = 1 \text{ s}$ is:

$A$ 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).

Which of the following is not a projectile?

$A$ body is projected from the ground at an angle $\theta_1$ with the horizontal with kinetic energy $K$. What is the potential energy of the body when the velocity makes an angle $\theta_2$ with the horizontal?

The coordinates of a moving particle at any time $t$ are given by $x = a\, t^2$ and $y = b\, t^2$. The speed of the particle is