In a sonometer wire the fundamental frequency of the wire is `260 Hz`. In sonometer the tension is maintained by suspending a `50.7 kg` mass. When the suspended mass is completely submerged in water the fundamental frequency becomes `240 Hz`. The suspended mass has a volume

Options

A. `0.002 m^(3)`
B. `0.0075 m^(3)`
C. `0.004 m^(3)`
D. `0.006 m^(3)`

Answer

B

Explanation

Fundamental frequency `= (v)/(2L)`
`260 = (v_(1))/(2L), 240 = (v_(2))/(2L)`
`(v_(1))/(v_(2))=sqrt((T_(1))/(T_(2)))=(260)/(240)=(13)/(12)`
`(T_(1))/(T_(2))=(169)/(144)`
`rArr (507)/(T_(2))=(169)/(144)`
`T_(2)=432`
Loss in weight `= 507-432`
`= 75`
`75=V rho g`
`rArr V=(75)/(rho g)=(75)/(10^(3)xx10)=0.0075 m^(3)`