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Question

The frequency of a sonometer wire is 100 Hz. When the weights producing the tensions are completely immersed in water, the frequency becomes 80 Hz and on immersing the weights in a certain liquid, the frequency becomes 60 Hz. The specific gravity of the liquid is

A
1.42
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B
1.77
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C
1.82
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D
1.21
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Solution

The correct option is A 1.77
As we know, frequency
fmg or fg
In water, fw=0.8fair
gf(0.8)2=0.64
1ρwρm=0.64
ρwρm=0.36....(1)
In liquid, gg=(0.6)2=0.36
1ρ1ρm=0.36ρ1ρm=0.64.....(2)
From eq. (1) and (2)
ρlρn=0.640.36ρl=1.77.

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