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A sonometer wire resonates with a given turning fork forming standing waves with five antinodes between two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by M, the wire resonates with the same tuning fork forming three antinodes for the same positions of bridges. The value of M (in kg) is
    Correct answer is '25'. Can you explain this answer?
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    A sonometer wire resonates with a given turning fork forming standing...
    As per the given condition,
    Or M = 25 kg
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    A sonometer wire resonates with a given turning fork forming standing...

    Given Data:
    - Number of antinodes with 9 kg mass: 5
    - Number of antinodes with mass M: 3

    Calculating the Mass M:
    - The number of antinodes in the standing wave pattern is inversely proportional to the square of the linear mass density of the string.
    - Let the linear mass density of the wire be λ.
    - When the mass is 9 kg, the number of antinodes is 5.
    - When the mass is M, the number of antinodes is 3.

    Calculating the ratio of linear mass density:
    - Since the frequency of the tuning fork is constant, the speed of the wave remains the same.
    - The speed of the wave is given by v = √(T/λ), where T is the tension in the wire.
    - Since the speed is constant, the linear mass density ratio is the same as the square of the antinode ratio.
    - (λ1/λ2)^2 = (5/3)^2 = 25/9

    Solving for M:
    - The mass M is inversely proportional to the linear mass density.
    - M1/M2 = λ2/λ1 = 9/25
    - M/9 = 9/25
    - M = 9 * 9/25
    - M = 81/25
    - M = 25 kg

    Therefore, the value of M is 25 kg.
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    A sonometer wire resonates with a given turning fork forming standing waves with five antinodes between two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by M, the wire resonates with the same tuning fork forming three antinodes for the same positions of bridges. The value of M (in kg) isCorrect answer is '25'. Can you explain this answer?
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    A sonometer wire resonates with a given turning fork forming standing waves with five antinodes between two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by M, the wire resonates with the same tuning fork forming three antinodes for the same positions of bridges. The value of M (in kg) isCorrect answer is '25'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sonometer wire resonates with a given turning fork forming standing waves with five antinodes between two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by M, the wire resonates with the same tuning fork forming three antinodes for the same positions of bridges. The value of M (in kg) isCorrect answer is '25'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sonometer wire resonates with a given turning fork forming standing waves with five antinodes between two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by M, the wire resonates with the same tuning fork forming three antinodes for the same positions of bridges. The value of M (in kg) isCorrect answer is '25'. Can you explain this answer?.
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