Question

the frequency of a sonometer wire is f.when the weight producing the tension are completely immersed in water the frequency becomes f/2 and on immersed the weight in certain liguid the frequency becomes f/3 the specific gravity of the liguid is

Answer 1

The specific gravity of the liquid is ​ρ  L = 32 / 27

Explanation:

• Frequency of a sono meter is given by

f= 1 / 2l √ Mg /m

Where l is the length an m is mass per unit length of the string.

• Frequency of the sonometer when the mass is immersed in water is

fw= 1 / 2l √ Mg- ρV(wg) / m

Here Vρg is the buoyancy force.

f(w) = f / 2 => 1 / 4l √Mg/m = 1 / 2l √Mg - Vρwg / m

Here ρw  = 1

Squaring both sides of the above equation, we get

V= M/4 =   M−V⇒V=M−M/4=  3M / 4

Frequency of the sonometer when the mass is immersed in the unknown liquid is.

fL = 1/2l  √Mg  - VρLg / m

fL = 1/ 6l √Mg / m = 1 /2l √Mg  - VρLg / m

Using the value of V from equation (1), we get

M /9 = M−Vρ  L

M /9 = M−  3M/4  ρ  L

ρ  L = 32 / 27

Hence the specific gravity of the liquid is ​ρ  L = 32 / 27

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