A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity . The force exerted by the liquid at the other end is

1. $\frac{1}{2}M{\omega }^2{L}^2$

2. ${\mathrm{M\omega }}^2\mathrm{L}$

3.$\frac{1}{4}M{\omega }^{2}L$

4. $\frac{1}{2}M{\omega }^{2}L$

 

Three long wires, each carrying current i are placed parallel to each other. The distance between I and II is 3d, between II and III is 4 d and between III and I is 5d. Magnetic field at side of wire II is 

1. $\frac{5{\mathrm{\mu }}_0\mathrm{i}}{24\mathrm{\pi d}}$

2. $\frac{10{\mathrm{\mu }}_0\mathrm{i}}{24\mathrm{\pi d}}$

3. $\frac{15{\mathrm{\mu }}_0\mathrm{i}}{24\mathrm{\pi d}}$

4. $\frac{20{\mathrm{\mu }}_0\mathrm{i}}{24\mathrm{\pi d}}$

In the following diagrams, a particle with small charge – q is free to move up or down, but not sideways near a larger fixed charge Q. The small charge is in equilibrium because in the positions shown, the electrical upward force is equal to the weight of the particle. Which statement is true? 

1. In figure a, -q is in stable equilibrium.

2. In figure a, -q is in neutral equilibrium.

3. In figure b, -q is in stable equilibrium.

4. Neither in fig(a) nor in fig(b) , q is in stable equilibrium.