The magnitude of the centripetal force acting on a body of mass $m$ executing uniform circular motion in a circle of radius $r$ with speed $v$ is:

$A$ particle is moving along a circular path of radius $R$ in such a way that at any instant the magnitude of radial acceleration and tangential acceleration are equal. If at $t = 0$ the velocity of the particle is $V_0$,the time period of the first revolution of the particle is:

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).

$A$ car is moving with a speed of $30 \ m/s$ on a circular path of radius $500 \ m$. Its speed is increasing at the rate of $2 \ m/s^2$. What is the acceleration of the car in $m/s^2$?

$A$ particle moves along a circle of radius $3 \, m$ with its displacement given by $S = \frac{t^2}{2} + \frac{t^3}{3}$. The total acceleration at $t = 2 \, s$ is ....... $m/s^2$.

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