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
B. 20
C. 15
D. 10

Answer

A

Explanation

`f=(sqrt((9g)/(mu)))/((2l)/(5))`
`f=(sqrt((Mg)/(mu)))/((2l)/(3))rArr f=(sqrt((9g)/(mu)))/((2l)/(5))=(sqrt((Mg)/(mu)))/((2l)/(3))rArr sqrt(M)=5`.