The fundamental frequency of a sonometer wire carrying a block of mass ' M ' and density ' ρ ' is ' n ' Hz. When the block is completely immersed in a liquid of density ' σ ' then the new frequency will be (a) n[(ρ - σ)/(ρ)]1/2 (b) n[(ρ - σ)/(σ)]1/2 (c) n[(ρ)/(ρ - σ)]1/2 (d) n[(σ)/(ρ - σ)]1/2

Answer: (a). n = 1/2l√(T/μ) ⇒ n ∝ √(T). In air T = Mg. Immersed: T' = Mg - M/ρσ g = Mg (ρ - σ)/(ρ). n' = n√(T'/T) = n[(ρ - σ)/(ρ)]1/2 So the answer is (a).

The fundamental frequency of a sonometer wire carrying a block of… | MHT CET 2023 (13 May, Shift 1)

Q11MHT CET 2023 · 13 MAY · SHIFT 1Difficult

Archimedes' Principle & Floatation

The fundamental frequency of a sonometer wire carrying a block of mass ' $M$ ' and density ' $\rho$ ' is ' $n$ ' Hz. When the block is completely immersed in a liquid of density ' $\sigma$ ' then the new frequency will be

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Answer: (a)

$n = \dfrac{1}{2l}\sqrt{\dfrac{T}{\mu}} \Rightarrow n \propto \sqrt{T}$ .
In air $T = Mg$ . Immersed: $T' = Mg - \dfrac{M}{\rho}\sigma g = Mg\,\dfrac{\rho - \sigma}{\rho}$ .
$n' = n\sqrt{\dfrac{T'}{T}} = n\left[\dfrac{\rho - \sigma}{\rho}\right]^{1/2}$
So the answer is (a).

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Archimedes' Principle & Floatation question from MHT CET 2023 (13 May, Shift 1)

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