The frequency of a sonometer wire is f , but when the weight 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

Step-by-step solution

f = 1 2 ℓ W μ ...(1) Now weight is immeresed in water. f 2 = 1 2 ℓ W - B μ ...(2) From (1) and (2) 1 2 × 1 2 ℓ W μ = 1 2 ℓ W - B μ ⇒ B = 3 4 W V ρ w g = 3 4 V ρ g ⇒ ρ w = 3 4 ρ ...(3) Now weight is immeresed in liquid. f 3 = 1 2 ℓ W - B ′ μ ...(4) From (1)and(4) B ′ = 8 9 W ⇒ V ρ ℓ g = 8 9 V ρ g ⇒ ρ ℓ = 8 9 ρ ...(5) From (3)and(5) ρ ℓ ρ w = 3 2 2 7