A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 $$\mu $$F. All values in the circuit are in $$\mu $$F.

A parallel plate capacitor with plates of area 1 m² each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is :

(Take $$\varepsilon $$₀ = 8.85 $$ \times $$ 10^$$-$$12 $${{{C^2}} \over {N - {m^2}}}$$)

A plano-convex lens (focal length f₂, refractive index $$\mu $$₂, radius of curvature R) fits exactly into a plano-concave lens (focal length f₁, refractive index $$\mu $$₁, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :