An athlete completes one round of a circular track of radius $10 \, m$ in $40 \, sec$. The distance covered by him in $2 \, min \ 20 \, sec$ is ........ $m$.

Two objects are projected at an angle $\theta^{\circ}$ and $(90-\theta)^{\circ}$ to the horizontal with the same speed. The ratio of their maximum vertical heights is

$A$ 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

Two identical discs of same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$. The discs are in the same horizontal plane. At time $t=0$,the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ as a function of time is best represented by:

The coordinates of a particle moving in the $x-y$ plane are given by: $x = 2 + 4t$,$y = 3t + 8t^2$. The motion of the particle is:

$A$ stone of mass $0.25 \; kg$ is tied to the end of a string and is being whirled in a horizontal circle of radius $1.5 \; m$ with a speed of $40 \; rev./min$. If the speed of the stone is increased beyond the maximum permissible value and the string breaks suddenly,which of the following correctly describes the trajectory of the stone after the string breaks?
$(a)$ The stone moves radially outward.
$(b)$ The stone flies off tangentially from the instant the string breaks.
$(c)$ The stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle.