$A$ particle of mass $m$ is projected at $45^o$ at $V_0$ speed from point $P$ at $t = 0$. The angular momentum of the particle about $P$ at $t = \frac{V_0}{g}$ is:

Two balls are projected from the same point simultaneously. The first ball is projected vertically upwards with velocity $u_1$ and the second ball at an angle of projection $60^{\circ}$ to the ground level with velocity $u_2$. Both the balls reach the ground simultaneously. The ratio of their velocities $u_1 : u_2$ is

$A$ particle is projected from a point at an angle $\theta$ with the horizontal direction. At any time $t$, if $p$ is the linear momentum, $y$ is the vertical displacement, and $x$ is the horizontal displacement, which of the following graphs does not represent the variation of kinetic energy $KE$ of the particle?

The coordinates of a moving particle at any time $t$ are given by $x = \alpha t^3$ and $y = \beta t^3$,where $\alpha$ and $\beta$ are constants. The speed of the particle at time $t$ is given by:

$A$ car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take the same time to complete the circles,the ratio of their angular speeds and linear speeds will be .........

The ratio of minimum kinetic energies of two projectiles of same mass is $4: 1$ and the ratio of maximum heights attained by them is $4: 1$. Then the ratio of their ranges is . . . . . . (in $: 1$)