Two stones of masses \(m\) and \(2m\) are whirled in horizontal circles, the heavier one in a radius \(\frac{r}{2}\) and the lighter one in a radius \(r\). The tangential speed of lighter stone is \(n\) times that of the value of heavier stone when they experience the same centripetal forces. The value of \(n\) is:
1. | \(3\) | 2. | \(4\) |
3. | \(1\) | 4. | \(2\) |
1. | \(\pi \over 3 \) | 2. | \(\pi \over 6\) |
3. | \(\pi \over 4\) | 4. | \(0^\circ\) |
1. | \(14\) m/s and \(15\) m/s |
2. | \(15\) m/s and \(16\) m/s |
3. | \(16\) m/s and \(17\) m/s |
4. | \(13\) m/s and \(14\) m/s |
A tube of length \( L\) is filled completely with an incompressible liquid of mass \(M\) and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity \(\omega\). The force exerted by the liquid at the other end is:
1. | \(ML \omega^2 \over 2\) | 2. | \(ML^2 \omega \over 2\) |
3. | \(ML \omega^2 \) | 4. | \(ML^2 \omega^2 \over 2\) |