A block is being hung in the air from a wire which is stretched over a sonometer. The bridges of the sonometer are L cm apart when the wire is in unison with a tuning fork of frequency N . When the block is completely immersed in water, the length between the bridges is e cm for re-establishing unison. The specific gravity of the material of the block is

Step-by-step solution

When the block is being hung in air N = 1 2 L M g μ ...(i) Now, consider the case when the block is in water T 1 + F B = M g ⇒ T 1 + ρ M σ g = M g ∴ T 1 = M g 1 - ρ σ Where σ : Density of block ρ : Density of water N = 1 2 e T 1 μ = 1 2 e M g 1 - ρ σ μ If σ ′ : specific gravity of block then from Eqs. (i) and (ii) e L = 1 - 1 σ ′ ⇒ e 2 L 2 = 1 - 1 σ ′ ⇒ 1 σ ′ = 1 - e 2 L 2 ⇒ σ ′ = L 2 L 2 - e 2