$A$ particle of mass $m$ is performing $U.C.M.$ along a circle of radius $r$. The relation between centripetal acceleration $a$ and kinetic energy $E$ is given by

In dealing with the motion of a projectile in the air,we ignore the effect of air resistance on the motion. This gives a trajectory that is a parabola,as you have studied. What would the trajectory look like if air resistance is included? Sketch such a trajectory and explain why you have drawn it that way.

When a body moves with a constant speed along a circle,

Two particles are projected from the same point with the same speed at different angles $\theta _1$ and $\theta _2$ to the horizontal. They have the same range. Their times of flight are $t_1$ and $t_2$ respectively.

The figure shows a sphere of mass $500 \ g$ moving in a steady flow of air in the $x$-direction. The air-stream exerts an essentially constant force of $0.9 \ N$ on the sphere in the $x$-direction. If at $t = 0$ the sphere is moving as shown in the figure,determine the time required for the sphere to cross the $y$-axis again in $\sec$. (in $.66$)

Will the linear velocity of a particle rotating with a constant angular speed about a non-fixed axis be constant? Why?