Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre (fixed) and at each stroke of the pump ∆V(<< V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from `P_1` to`P_2`.

Why does a tyre can be inflated with large volume of air ?

A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body frm the centre of the star and let its linear velocity be v, angular velocity omega , kinetic energy K, gravitational potential energy U, total energy E and angular momentum p. As the radius r of the orbit increases, determine which of the above quantities increase and which one decrease.

When air is pumped into a cycle tyre the volume and pressure of the air in the tyre both are increased. What about Boyle's law in this case?

The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilo litres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

Let G_(1), G(2) and G_(3) be the centroid of the triangular faces OBC, OCA and OAB of a tetrahedron OABC. If V_(1) denotes the volume of tetrahedron OABC and V_(2) that of the parallelepiped with OG_(1), OG_(2) and OG_(3) as three concurrent edges, then the value of (4V_(1))/(V_2) is (where O is the origin

Two identical plane metallic surfaces A and B are parallel to each other in air separated by a distance of 1 cm as shown in the fig. Surface A is given a postive potential 10 V and the outer surface of B is earthend What is the magnitude and direction of the uniform electric field between points Y and Z?

A parallel plate capacitor of plate area A and plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted), and work done on the system, in question, in the process of inserting the slab,

Figure shows two identical capacitors C_1 and C_2 each of 1 mu F capacitance connected to a battery of 6 V. initially switch S is closed. After sometime S is left open and dielectric slab of dielectric constant k = 3 are inserted to fill completely the space between the plates of the two capacitors. How will the Charge between the plates of the capacitors be affected after the slabs are inserted?

An engine pumps out water continously through a hose with a veclocity v.If m is the mass per unit length of the water jet ,the rater at which the kinetic energy is imparted to water is :

Two men A and B start with velocities v at the same time from the junction of two roads inclined at 45^@ to each other. If they travel by different roads, find the rate at which they are being separated.