A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $$\omega $$ rad s^–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be :

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

A small spherical droplet of density d is floating exactly half immersed in a liquid of density $$\rho $$ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :

Water flows in a horizontal tube (see figure).
The pressure of water changes by 700 Nm^–2
between A and B where the area of cross section
are 40 cm² and 20 cm², respectively. Find the
rate of flow of water through the tube.
(density of water = 1000 kgm^–3)