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Sonometer wire resonates with a fork with some antinodes under one mass and fewer antinodes under mass M; find M

The same question, asked 3 times: 15 Apr 2026 S1*, 12 May 2026 S2, 19 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    15 Apr 2026 S1

    123
    A sonometer wire resonates with 44 antinodes between the two bridges for a given tuning fork when 11 kg mass is suspended from the wire. Using same fork, when mass M is suspended, the wire resonates producing 22 antinodes between the two bridges. (Distance between the bridges as before) The value of M is

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  2. Question 2

    12 May 2026 S2

    124
    A sonometer wire resonates with a given tuning fork forming standing wave with 55 antinodes between two bridges when mass of 99 kg is suspended from the wire. When mass MM is suspended from the wire with same fork and same length between two bridges, 33 antinodes are formed. Mass MM is

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  3. Question 3

    19 May 2026 S2

    122
    A sonometer wire resonates with a given tuning fork, forming standing waves with five antinodes between the two bridges, when a mass of 99 kg is suspended from the wire. When this mass is replaced by mass MM, the wire resonates with the same tuning fork, forming three antinodes for the same positions of the bridges. The value of MM (in kg) is

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