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Question: The frequency of sonometer wire is f, but when the weights producing the tensions are completely imm...

The frequency of sonometer wire is f, but when the weights producing the tensions are completely immersed in water the frequency becomes f/2 and on immersing the weights in a certain liquid the frequency becomes f/3. The specific gravity of the liquid is –

A

43\frac{4}{3}

B

169\frac{16}{9}

C

1512\frac{15}{12}

D

3227\frac{32}{27}

Answer

3227\frac{32}{27}

Explanation

Solution

f = 12lTm\frac{1}{2\mathcal{l}}\sqrt{\frac{T}{m}} ... (1)

f2\frac{f}{2}= 12l\frac{1}{2\mathcal{l}} T−ρ2Vgm\sqrt{\frac{T - \rho_{2}V_{g}}{m}} ... (2)

rw ® density of water

f3\frac{f}{3}=12l\frac{1}{2\mathcal{l}} T−ρ2Vgm\sqrt{\frac{T - \rho_{2}V_{g}}{m}} ... (3)

rL ® density of liquid

T = Vrg ® r ® density of block

from (1) and (2) r = 43\frac{4}{3} rw

from (1) and (3) ρLρW=3227\frac{\rho_{L}}{\rho_{W}} = \frac{32}{27}