Two narrow cylindrical pipes A and B have the same length Pipe A is open at both ends and is filled with a monoatomic gas of molar mass M Pipe B is open at opne end and closed at the other end and is filled with a diatomic gas of molar mass M Both gases are at the same temperature a If the frequency of the second harmonic of the fundamental mode in Pipe Als equal to the frequency of the third harmonic of the fundamental mode in pipe B determine the value of M MB b Now the opeen end to pipe B is also closed so that the pipe is closed at both ends Find the ratio of the fundamental frequency in pipe A to that in pipe B 3 2 A cubical box of side 1 meter contains hellum gas atomic weight 4 at a pressure of 100N m During an observation time of 1 second an atom travelling with the root mean square speed parallel to one of the edges of the cube was found to make 500 hits with a particular wall wolthout any collision with other atoms Take R J mol K andk 1 38x10 J K a Evaluate the temperature of the gas b Evaluate the average kinetic energy per atom c Evaluate the total mass of helulm gas in the box A uniform solld cylinder of density 0 8 g cm floats in equilibrium in a combination of two non mixing liquids A and B with its axis vertical The densities of the liquids A and B are 0 7 g cm and 1 2 g cm respectively The height of liquid A is h 1 2 cm The length of the part of the cylinder Immersed in liquid B Ish 0 8 cm a Find the total force exerted by liquid A on the cylinder air A thin uniform wire AB of length 1m an unknown resistance X and a resistance of 1202 are connected by thick conducting strips as shown in A B 2 1 2 b Find h the length of the part of teh cylinder in air c The cylinder is depressed in such a way that is top surface is just below the upper surface of liquid A and is then released Find the acceleration of the cylinder immediately after it is released 1 2 2 ha 120