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. `25kg`
B. `5kg`
C. `12.5kg`
D. `1/25kg`

Answer

A

Explanation

The frequency of vibration of string is given by
`v=p/(2L)sqrt(T/m)`
where `P=` number of loops
`=` number of antinodes
According to the question
`5/(2L)sqrt((9g)/m)=3/(2L)sqrt((Mg)/m)` or `M=25kg`