$A$ 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 $\pi = \frac{22}{7}$)

$A$ cyclist is riding with a speed of $27 \; km/h$. As he approaches a circular turn on the road of radius $80 \; m$,he applies brakes and reduces his speed at the constant rate of $0.50 \; m/s^2$. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

Explain the effects of the radial component and the tangential component of the linear acceleration of a particle in circular motion.

$A$ particle moves on a circular path with decreasing speed. Identify the correct statement.

In a circular motion of a particle,the tangential acceleration of the particle is given by $a_t = 12 \ m/s^2$. The radius of the circle is $3 \ m$. The particle was initially at rest. The time after which the total acceleration of the particle makes an angle $45^{\circ}$ with the radial acceleration is

For a particle in a uniformly accelerated circular motion: