IIT-JEE-Physics-Mains-2002

MAIN
Time : Two hours                                        Max. Marks : 60
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Instructions
1.     The Question Paper has 4 printed pages and has 12 questions. Please ensure that the copy of the Question Paper you have received contains all the questions.
2.     Attempts ALL questions. Each question carries 5 marks.
3.     Answer each question starting on a new page. The corresponding Question number must be written in the left margin.
4.     Do not write more than one answers for the same question. In case you attempt a question more than once, please cancel the answer(s) you consider to be wrong. Otherwise, only the answer appearing last will be evaluated.
5.     Use only Arabic numerals (0, 1, 2 .............9) in answering the questions irrespective of the language in which your answer.
6.     Use of logarithmic tables is NOT PERMITTED.
7.     Use of calculators is NOT PERMITTED.
8.     Both magnitude and direction of vector quantities, if any, in your answer should be indicated clearly.
9.     Irrational numbers, if any, in your answer need not be expressed in decimal form.
10.  If the final answer appears in the form of a ratio or a product of two numbers, that need not to be further simplified.
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1.         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_A. Pipe B is open at one end and closed at the other end, and is filled with a diatomic gas of molar mass M_B. Both gases are at the same temperature.
(a)       If the frequency to the second harmonic of the fundamental mode in ppe A is equal of the frequency of the third harmonic of the fundamental mode in pipe B, determine the value of M_A/M_B.
(b)       Now the open end of 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.

2.         A cubical box of side 1 meter contains helium gas (atomic weight 4) at a pressure of 100 N/m². During an observation time of 1 second, an atom travelling with root-mean-square speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. Take R = 25/3 J/mol-K and k = 1.38 × 10^-23 J/K.
            (a)       Evaluate the temperature of the gas.
            (b)       Evaluate the average kinetic energy per atom.
            (c)        Evaluate the total mass of helium gas in the box.

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IIT-JEE-Physics-Mains-2002

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