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 \({{20}\over{\pi}} m\) 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. 640π ms–2
3. 160π ms–2
4. 40π 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?
1. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the tangent to the circle. |
2. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the radius towards the centre. |
3. | \(\frac{\pi^2}{4} \mathrm{~ms}^{-2}\) and direction along the radius towards the centre. |
4. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the radius away from the centre. |