A ideal gas is kept in a cylinder of cross sectional area A and volume `v_0`. The mass of the gas enclosed is M and bulk modulus B. If the piston of the cylinder is pressed by small x, then find the time period of small oscillations,

An air chamber of volume V has a long of cross setional area A.A ball of mass m is fixted smpthlly in the track The ball modulus of air is B ball is pressed down slightly and released, the time period of the oscillation is

An ideal gas is enclosed in a cylinder having cross sectional area A. The piston of mass M has its lower face inclined at theta to the horizontal. The lower face of the piston also has a hemispherical bulge of radius r. The atmospheric pressure is P_(0) . (a) Find pressure of the gas. (b) The piston is slowly pulled up by a distance x. During the process the piston is always maintained in equilibrium by adding heat to the gas. [It means if the piston is left at any stage it will stay there in equilibrium]. Find change in temperature of the gas. Number of mole of the gas in the cylinder is one.

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. the piston and the cylinder have equal cross sectional area A. when the piston is in equilibrium, the volume of the gas is V_(0) and its pressure is P_(0) . the piston is slightly displaced from the equilibrium posittion and released. assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10cm^(2) and weight 1kg. The length of the gas column in the vessel mow taken into a spaceship revolving round the earth as satellite. The air pressure in the spaceship is amintained at 100kPa. Find the length of the gas column in the cylinder.

An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10cm^(2) and weight 1kg. The length of the gas column in the vessel now taken into a spaceship revolving round the earth as satellite. The air pressure in the spaceship is maintained at 100kPa. Find the length of the gas column in the cylinder.

A gas is filled in a cylinder with initial pressure P, initial volume V. When the pressure is increased by dP and volume reduces by dV. The bulk modulus is

A uniform plank of mass m, free to move in the horizontal direction only , is placed at the top of a solid cylinder of mass 2 m and radius R. The plank is attached to a fixed wall by mean of a light spring constant k. There is no slipping between the cylinder and the planck , and between the cylinder and the ground. Find the time period of small oscillation of the system.

A uniform plank of mass m, free to move in the horizontal direction only , is placed at the top of a solid cylinder of mass 2 m and radius R. The plank is attached to a fixed wall by mean of a light spring constant k. There is no slipping between the cylinder and the planck , and between the cylinder and the ground. Find the time period of small oscillation of the system.

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. The time period of oscillation for small displacements of the piston is