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The frequency of sonometer wire is f. Th...

The frequency of sonometer wire is f. The frequency becomes `f//2` when the mass producing the tension is completely immersed in water and on immersing the mass in a certain liquid, frequency becomes `f//3`. The relative density of the liquid is

A

0.32

B

1.67

C

1.41

D

1.18

Text Solution

Verified by Experts

The correct Answer is:
D
`f prop sqrtT`
`f/(f//2) = sqrt(T_1/T_2) = sqrt(W/(W-V_1))`
`2 = sqrt ((vrhog)/(Vrhog - Vrho_wg)) = sqrt (rho/(rho - rho_w))`
Solving `rho=4/3 rho_w`
`f/(f//3) = sqrt(W/(W-V_2)) = sqrt((Vrhog)/(vrhog-Vrho_lg))`
`9= (rho/(rho-rho_1))`
`:. rho_l = 8/9 rho = 32/27 rho_w`
`:.` Relative density of liquid = `rho_l/rho_w`
=`32/27 = 1.18` .
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