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 :

Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light source ($$\lambda $$ = 632.8 nm). The distance between the screen and the slits is 100 cm. If a bright fringe is observed on a screen at a distance of 1.27 mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close is

A 5 $$\mu $$F capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 $$\mu $$F capacitor. If the energy change during the charge redistribution is $${X \over {100}}J$$ then value of X to the nearest integer is _____.

A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 $$ \times $$ 10^–5 T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in $$\mu $$V) in the coil will be close to the integer _______.