The hour hand of a clock is $6\,cm$ long. The magnitude of the displacement of the tip of the hour hand between $1:00\,PM$ and $5:00\,PM$ is:

The range of a projectile is $100 \ m$. Its kinetic energy will be maximum after covering a horizontal distance of: (in $m$)

Three particles start simultaneously from a point on a horizontal smooth plane. The first particle moves with speed $v_1$ towards the east,the second particle moves towards the north with speed $v_2$,and the third one moves towards the north-east. The velocity of the third particle,such that the three particles always lie on a straight line,is

Two particles $A$ and $B$ start at the origin $O$ and travel in opposite directions along a circular path of radius $0.5\,m$ at constant speeds $0.5\,m/s$ and $1.5\,m/s$,respectively. The time when they collide with each other is ........ $\text{s}$.

For a given initial velocity,a projectile is fired at angles of $30^\circ$ and $60^\circ$. Find the ratio of their maximum heights.

$A$ particle is projected from a point at an angle $\theta$ with the horizontal direction. At any time $t$, if $p$ is the linear momentum, $y$ is the vertical displacement, and $x$ is the horizontal displacement, which of the following graphs does not represent the variation of kinetic energy $KE$ of the particle?