$A$ stone tied to a $180 \, cm$ long string at its end is making $28$ revolutions in a horizontal circle in every minute. The magnitude of the acceleration of the stone is $\frac{1936}{x} \, m s^{-2}$. The value of $x$ is: (Take $\pi = \frac{22}{7}$)

$A$ 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 $.............$.

For a particle in circular motion,the centripetal acceleration is

An object is moving on a circular track of radius $450\, m$. At some instant,the object is moving at $30\, m/s$ and gaining speed at a uniform rate of $2\, m/s^2$. Its acceleration at this instant is nearly .......... $m/s^2$.

An electron is moving in a circle of radius $2 \, m$ with a speed of $4 \, m/s$. Find the acceleration of the electron in $m/s^2$.

$A$ point object moves along an arc of a circle of radius $R$. Its velocity depends upon the distance covered $s$ as $v=K \sqrt{s}$,where $K$ is a constant. If $\theta$ is the angle between the total acceleration and tangential acceleration,then