A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5s, is close to :

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 :

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

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)