$A$ wheel completes $2000$ rotations in covering a distance of $9.5\,km$. The diameter of the wheel is:

Show that for a projectile,the angle between the velocity and the $x$-axis as a function of time is given by $\theta(t) = \tan^{-1}\left(\frac{v_{0y} - gt}{v_{0x}}\right)$.
Show that the projection angle $\theta_0$ for a projectile launched from the origin is given by $\theta_0 = \tan^{-1}\left(\frac{4h_m}{R}\right)$,where the symbols have their usual meanings.

$A$ 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:

$A$ plane is revolving around the Earth with a speed of $100\, km/hr$ at a constant height from the surface of the Earth. The change in the velocity as it travels a half circle is ......... $km/hr$.

Two particles of equal masses are revolving in circular paths of radii $r_1$ and $r_2$ respectively with the same speed. The ratio of their centripetal forces is

$A$ stone of mass $m$ is tied to a string of length $l$ and rotated in a circle with a constant speed $v$. If the string is released,the stone flies: