MHT CET · Physics · Waves and Sound
A sonometer wire under suitable tension having specific gravity ' \(\varrho^{\prime}\), vibrates with frequency 'n' in air. If the load is completely immersed in water the frequency of vibration of wire will become
- A \(\left[\frac{0-1}{n \varrho}\right]^{\frac{1}{2}}\)
- B \(n\left[\frac{\varrho}{0-1}\right]^{\frac{1}{2}}\)
- C \(\left[\frac{n \varrho}{0-1}\right]^{\frac{1}{2}}\)
- D \(n\left[\frac{0-1}{\varrho}\right]^{\frac{1}{2}}\)
Answer & Solution
Correct Answer
(D) \(n\left[\frac{0-1}{\varrho}\right]^{\frac{1}{2}}\)
Step-by-step Solution
Detailed explanation
\((\mathrm{C})\)
\(\mathrm{T}_{1}=\mathrm{mg}=\mathrm{v} \rho \mathrm{g}\)
\(\mathrm{T}_{2}=\mathrm{v}(\rho-\sigma) \mathrm{g} \quad \sigma=1\) for water
\(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\mathrm{vpg}}{\mathrm{v}(\rho-1) \mathrm{g}}=\frac{\rho}{\rho-1}\)
\(\therefore \frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\sqrt{\frac{\rho}{\rho-1}} \quad \therefore \mathrm{n}_{2}=\mathrm{n}_{1} \sqrt{\frac{\rho-1}{\rho}}\)
\(\mathrm{T}_{1}=\mathrm{mg}=\mathrm{v} \rho \mathrm{g}\)
\(\mathrm{T}_{2}=\mathrm{v}(\rho-\sigma) \mathrm{g} \quad \sigma=1\) for water
\(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\mathrm{vpg}}{\mathrm{v}(\rho-1) \mathrm{g}}=\frac{\rho}{\rho-1}\)
\(\therefore \frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\sqrt{\frac{\rho}{\rho-1}} \quad \therefore \mathrm{n}_{2}=\mathrm{n}_{1} \sqrt{\frac{\rho-1}{\rho}}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Three identical polaroids \(P_1, P_2\) and \(P_3\) are placed one after another. The pass axis of \(\mathrm{P}_2\) and \(P_3\) are inclined at an angle \(60^{\circ}\) and \(90^{\circ}\) with respect to axis of \(\mathrm{P}_1\). The source has an intensity \(I_0\). The intensity of transmitted light through \(P_3\) is \(\left(\cos 60^{\circ}=0.5, \cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)\)MHT CET 2024 Easy
- The angle subtended by the vector \(\vec{A}=4 \hat{\imath}+3 \hat{\jmath}+12 \hat{k}\) with the \(\mathrm{x}\) -axis isMHT CET 2020 Easy
- If the spherical planet of mass ' \(\mathrm{M}^{\prime}\) and radius 'R' suddenly shrinks to half its size, its mass reduces to half. The new moment of inertia of the planet about its diameter isMHT CET 2020 Easy
- Initially n identical capacitors are joined in parallel and are charged to potential V. Now they are separated and joined in series. ThenMHT CET 2025 Medium
- To determine the internal resistance of a cell by using a potentiometer, the null point is at \(1 \mathrm{~m}\) when the cell is shunted by \(3 \Omega\) resistance and at a length \(1.5 \mathrm{~m}\) when cell is shunted by \(6 \Omega\) resistance. The internal resistance of the cell is.MHT CET 2022 Medium
- Select the correct statement.MHT CET 2025 Medium
More PYQs from MHT CET
- Figure show the circular coil carrying current kept very close but not touching at a point A on a straight conductor carrying the same current . The magnitude of magnetic induction at the centre of the circular coil will be
MHT CET 2019 Medium - Theory of germplasm was proposed by _________ .MHT CET 2023 Easy
- Which one of the following organ has become vestigeal in man due to eating cooked food over many years?MHT CET 2023 Easy
- The points \(A(-a,-b)\), B \((0,0), C(a, b)\) and \(D\left(a^{2}, a b\right)\) areMHT CET 2020 Easy
- Barrier potential of a \(p-n\) junction diode does not depend onMHT CET 2007 Hard
- \(\int \frac{x^{2}+1}{x^{4}+x^{2}+1} d x=\)MHT CET 2020 Hard