The tube AC forms a quarter circule in a vertical plane. The ball B has an area of cross - section slightly smaller than that of the tube and can move without friction through it. B is placed at A and displaced slightly. It will

The narrow tube AC forms a quarter circles in a vertical plane. A ball B has an area of cross-section slighly smaller than that of the tube and can move without friction through it. B is placed at A and displaced slightly. During the motion from A to C it will :

(i) Air (density= rho ) flows through a horizontal venturi tube that discharges to the atmosphere. The area of cross section of the tube is A_(1) and at the constriction it is A_(2) . The constriction is connected to a water (density =rho_(0) ) tank through a vertical pipe of lenght H. Find the volume flow rate (Q) of the air through tube that is needed to just draw the water into the tube. (ii) A non viscous liquid of constant density rho flows in a stremline motion along a tube of variable cross section. The tube is kept inclined in the vertical plane as shown in the figure. The area of cross section of the tube at two points P and Q at heights of h_(1) and h_(2) are respectively A_(1) and A_(2) . The velocity of the liquid at point P is v. Find the work done on a small volume DeltaV of fluid by the neighbouring fluid as the small volume moves from P to Q.

A ball of mass m is moved with speed v_0 at the highest point in a closed circular tube of radius R kept in the vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.

A closed and isolated cylinder contains ideal gas. An adiabatic separator of mass m, cross sectional area A divides the cylinder into two equal parts each with volume V_(0) and pressure P_(0) in equilibrium Assume the sepatator to move without friction. If the piston is slightly displaced by x, the net force acting on the piston is

The volume V of a liquid crossing through a tube is related to the area of cross-section A, velocity v and times t as V alpha A^a v^b t^c which of the following is correct ( given a != 1 )