A sonometer wire resonates with a given tuning fork forming a standing wave with five antinodes between the two bridges when a mass of `9 kg` is suspended from the wire. When this mass is replaced by a mass 'M' kg, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. Find the value of `M`.

Options

A. 25 kg
B. 5 kg
C. 12.5 kg
D. `(1)/(25)kg`

Answer

D

Explanation

The frequency of vibration of a string is given by `upsilon=(p)/(2l)sqrt((T)/(mu))`
where p = number of loops (or segments) = number of antinodes and the other symbols have their usual meanings.
According to question, `(5)/(2l)sqrt((9g)/(mu))=(3)/(2l)sqrt((Mg)/(mu))orM=25kg`