A sonometer wire resonates with a given tuning fork forming standing waves with five antitodes between the two bridges when a mass of `9kg` is suspended from the wire. when this same tuning fork forming three antitodes 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=9gimpliesn_1=(5)/(2l)sqrt((9g)/(m))`
With 3 antinodes and hanging mass `M`
we have `p=3` and `T=Mgimpliesp_2=(3)/(2l)sqrt((Mg)/(m))`
`:. n_1=n_2implies(5)/(2l)sqrt((9g)/(m))=(3)/(2l)sqrt((Mg)/(m))impliesM=25Kg`