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Question

The fundamental frequency of a sonometer wire decreases by 25% when the body suspended at the free end of a wire is totally immersed in water. The specific gravity of that suspended body is :

A
25/9
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B
16/7
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C
7/3
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D
4
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Solution

The correct option is C 16/7
The natural frequency of nth mode is
fn=n2LTμ
where
L is the length of the sonometer wire, μ is the mass per unit length of the wire, T is the tension in the string
Frequency of the first harmonic before :f=12LTμ .....(1)
Frequency of the first harmonic after :f=12LTμ .......(2)
When the body suspended at free end of wire is totally immersed in water, T decreases because of buoyancy
TT=Fbuoyancy
VρgT=Vρwg where T=Vρg is the weight of the body and V is the volume of the body and ρ is the density of the body.
Dividing (1) by (2)

ff=TT=VρgVρgVρwg
(ff)2=(0.751)2=1ρwρ
ρwρ=1916=716
ρρw=167

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