Oil of density `800 kg/m^3` is flowing through a horizontal pipe line. At two points separated by a distance of 1km pressure difference is 5`N/m^3`. Calculate the change in KE per kg of the oil flowing at these points.

Water flows horizontally through a pipeline of varying cross-section. At two points A and B, the diameters are 0.6 m and 0.2m. The pressure difference between the points is 1m. Column of water. Calculate the volume of water flowing per second.

Water is flowing steadily through a horizontal pipe of non- uniform cross-section. The pressure of water is 4xx10^4 at a point, where cross-section is 0.02m^2 and velocity of flow is 2ms^-1 . What is the pressure at a point, where cross-section reduces to 0.01m^2 ?

Two bodies whose masses are m_1 = 50 kg and m_2 150g are tight by a string and placed in a horizontal surface. When m_1 is pulled by a force F and acceleration of 5ms^-2 is produced in both the bodies. Calculate the value of F and tension in the strong.

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm^2 . Calculate the elongation of the wire when the mass is at the lowest point of its path.

Two parallel Co-axial Coils of equal radius R and- numbers of turn N carrying equal currents I in same direction.are separated by a distance | R. Show that the magnetic field intensity B on the axis around the mid point between the coils is uniform over a very small distance as compared to R and is given by- B = (4/5)^(3/2) (mu_0IN)/R

A sphere of radius 0.25mm and of density 9000kg/m^3 falls through an oil of co-efficient of viscosity 0.2 Ns/m^2 and of density 800kg/m^3 . Find the terminal velocity of the sphere.

Two point charges of +3 *10^-19C and +2 * 10^-19 C are separated by a distance of 2.5m. Find the point on the line joining them at which electric intensity is zero.

Two particles, each of mass m and speed v_3 travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.