The diameter of a car wheel is $60 \ cm$. How many radians of angular displacement will the wheel have undergone while the car travels a distance of $1.2 \ km$?

$A$ particle of mass $m$ is projected at a velocity $u$, making an angle $\theta$ with the horizontal ($x$-axis). If the angle of projection $\theta$ is varied keeping all other parameters same, then the magnitude of angular momentum $(L)$ at its maximum height about the point of projection varies with $\theta$ as,

The position vector of a particle is given as $\vec{r} = (t^2 - 8t + 12)\hat{i} + t^2\hat{j}$. The time after which the velocity vector and acceleration vector become perpendicular to each other is equal to ........ $sec$.

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?

$A$ body of mass $m$ is projected at an angle of $45^{\circ}$ with the horizontal with an initial velocity $v$. If air resistance is negligible,then the total change in momentum when it strikes the ground is:

$A$ car runs at a constant speed on a circular track of radius $100\,m$,taking $62.8\,s$ for every circular lap. The average velocity and average speed for each circular lap respectively are: