Two particles having mass \(M\) and \(m\) are moving in a circular path having radius \(R\) & \(r\) respectively. If their time periods are the same, then the ratio of angular velocities will be: 
1. \(\frac{r}{R}\)
 2. \(\frac{R}{r}\)
3. \(1\)
4. \(\sqrt{\frac{R}{r}}\)

A particle moves along a circle of radius \(\frac{20}{\pi}~\text{m}\) with constant tangential acceleration. If the velocity of the particle is \(80\) m/s at the end of the second revolution after motion has begun, the tangential acceleration is:

1. \(40\) ms^–2

2. \(640\pi\) ms^–2

3. \(160\pi\) ms^–2

4. \(40\pi\) ms^–2

A stone tied to the end of a \(1\) m long string is whirled in a horizontal circle at a constant speed. If the stone makes \(22\) revolutions in \(44\) seconds, what is the magnitude and direction of acceleration of the stone?