$A$ 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

$A$ particle moves in a circle of radius $R$,with a constant speed $v$. Then,during a time interval $t = \pi R / 3v$,which of the following is true?

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown in the figure. The time of flight $T$ is given by ........ $\text{s}$.

$A$ point moves in the $xy$-plane according to the following equations: $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$, where $a$ and $\omega$ are positive constants. Find the angle between the point's velocity and acceleration vectors.

The given diagram shows a straight length of tape being wound on to a reel. The reel is rotating about a fixed axis with constant angular velocity and its radius is increasing at a steady rate. Which graph correctly shows the variation with time of the speed $v$ at which the tape moves towards the roll?

An object of mass $m$ is projected with a momentum $p$ at such an angle that its maximum height is $\frac{1}{4}$th of its horizontal range. Its minimum kinetic energy in its path will be