If $\omega_1$ is the angular velocity of the hour hand of a clock and $\omega_2$ is the angular velocity of the Earth,then the ratio $\omega_1 : \omega_2$ is

$A$ point $P$ is moving in uniform circular motion with radius $3 \ m$. Let at some instant the acceleration of the point be $a = (6 \hat{i} - 4 \hat{j}) \ m/s^2$, the position vector be $r$, and the velocity vector be $v$. Choose the correct statement.

$A$ stone tied to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolutions in $44$ seconds,what is the magnitude and direction of the acceleration of the stone?

The angle between velocity and acceleration of a particle describing uniform circular motion is (in $^{\circ}$)

$A$ particle is moving on a circular path with constant speed $v$. It moves between two points $A$ and $B$,which subtend an angle $60^{\circ}$ at the centre of the circle. The magnitude of the change in its velocity and the change in the magnitude of its velocity during motion from $A$ to $B$ are respectively ..........

$A$ ball is moving uniformly in a circular path of radius $1 \, m$ with a time period of $1.5 \, s$. If the ball is suddenly stopped at $t = 8.3 \, s$,the magnitude of the displacement of the ball with respect to its position at $t = 0 \, s$ is closest to .......... $m$.