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 radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is-

1. 2

2. 3

3. 4

4. 1

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 ω. The force exerted by the liquid at the other end is:

1. $\frac{ML{\omega }^2}{2}$

2. $\frac{M{L}^2\omega }{2}$

3. $ML{\omega }^2$

4. $\frac{M{L}^2{\omega }^2}{2}$