A sonometer wire resonates with a given tuning fork forming ` 5` antinodes when a mass of `9 kg` is suspended from the wire . When this resonates with the same tuning fork forming three antinodes for the same positions of the bridges . The value of `M` is

Options

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

Answer

A

Explanation

The frequency of vibration of a string `n=p/(2l)sqrt(T/m)`
Also number of loops = Number of antinodes.
Hence, with 5 antinodes and hanging mass of 9 kg.
We have p = 5 and T = 9g `rArr n_1=5/(2l)sqrt((9g)/m)`
With 3 antinodes and hanging mass M
We have p=3 and T=Mg `rArr n_2=3/(2l)sqrt((Mg)/m)`
`because n_1=n_2 rArr 5/(2l) sqrt((9g)/m) =3/(2l)sqrt((Mg)/m)`
M=25