Water from a tap emerges vertically downwards with an initial speed of 1.0 ms^–1 . The cross-sectional area of the tap is 10^–4 m². Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be : (Take g = 10 ms^–2)

One mole of ideal gas passes through a process where pressure and volume obey the relation $$P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]$$. Here P₀ and V₀ are constants. Calculate the change in the temperature of the gas if its volume changes form V₀ to 2V₀

Space between two concentric conducting spheres of radii a and b (b > a) is filled with a medium of resistivity $$\rho $$. The resistance between the two spheres will be :

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is, R_L = 4k$$\Omega $$. The series resistance of the circuit is R_i = 1 k$$\Omega $$. If the battery voltage V_B varies from 8 V to 16 V, what are the minimum and maximum values of the current through Zener diode?