In non-uniform circular motion,the ratio of tangential to radial acceleration is ($r$ is the radius of the circle,$v$ is the speed of the particle,$\alpha$ is the angular acceleration).

$A$ disc is rotating with constant angular velocity $\omega$ about an axis passing through centre $C$ and perpendicular to the plane of the disc. An insect is moving over the disc along the radial direction with constant velocity $v$ with respect to the disc. The acceleration of the insect at the instant when its distance from the centre is $r$ will be :-

$A$ particle moves in a circular path with decreasing speed. Determine the correct statement.

$A$ particle moves along an arc of a circle of radius $R$. Its velocity depends on the distance covered as $v = a\sqrt{s}$,where $a$ is a constant. Then the angle $\alpha$ between the vector of the total acceleration and the vector of velocity as a function of $s$ will be:

$A$ car is travelling with linear velocity $v$ on a circular road of radius $r$. If it is increasing its speed at the rate of $a \ m/s^2$,then the resultant acceleration will be

$A$ car is moving with a speed of $30 \,ms^{-1}$ on a circular path of radius $500 \,m$. If its speed is increasing at the rate of $2 \,ms^{-2}$, then find its acceleration. (in $\,ms^{-2}$)