$A$ ring of mass $m$ moves from point $1$ to point $2$ along a smooth rigid horizontal wire with a constant speed $v$. The average force acting on the ring over the time of its motion from $1$ to $2$ is

$A$ wheel of radius $R$ is trapped in a mud pit and spinning. As the wheel is spinning,it splashes mud blobs with initial speed $u$ from various points on its circumference. The maximum height from the centre of the wheel,to which a mud blob can reach is

$A$ particle of mass $10\, g$ moves along a circle of radius $6.4\, cm$ with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{-4}\, J$ by the end of the second revolution after the beginning of the motion? .............. $m/s^2$

$A$ body of mass $0.6 \, kg$ is moving along a circular path of radius $1 \, m$. If the body moves with $\frac{900}{\pi}$ revolutions per minute, its kinetic energy is: (in $ \, J$)

$A$ particle moves in the $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$,where $a$ and $\omega$ are constants. The particle traces:

$A$ ball is thrown horizontally from a height with a certain initial velocity at time $t=0$. The ball bounces repeatedly from the ground with the coefficient of restitution less than $1$ as shown below. Neglecting air resistance and taking the upward direction as positive,which figure qualitatively depicts the vertical component of the ball's velocity $v_y$ as a function of time $t$?