In non-uniform circular motion, the ratio of radial acceleration to tangential acceleration is (where $V$ is the velocity, $r$ is the radius, and $\alpha$ is the angular acceleration).

$A$ particle is moving in a circle of radius $R$ with constant speed $v$. If the radius is doubled while keeping the speed the same,what happens to the centripetal force?

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

$A$ car is moving on a circular path of radius $600\,m$ such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete the first quarter of a revolution,if it is moving with an initial speed of $54\,km/h$,is $t(1 - e^{-\pi/2})\,s$. The value of $t$ is $.............$.

$A$ 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 $\,ms^{-2}$)

The force required to keep a body in uniform circular motion is: