MHT CET · Physics · Waves and Sound
A stretched uniform wire of length L under tension \(\mathrm{T}\) is vibrating with frequency
'n'. A closed pipe of same length is also vibrating with same fundamental frequency
'n'. If \(\mathrm{T}\) is increased by \(16 \mathrm{~N}\), it is in resonance with \(2^{\text {nd }}\) harmonic of same closed
pipe. The initial tension in the wire is
- A \(1 \mathrm{~N}\)
- B \(2 \mathrm{~N}\)
- C \(1 \cdot 5 \mathrm{~N}\)
- D \(0 \cdot 5 \mathrm{~N}\)
Answer & Solution
Correct Answer
(B) \(2 \mathrm{~N}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{n}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}=\frac{\mathrm{v}}{4 \ell}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}+16}{\mathrm{n}}}=\frac{3 \mathrm{v}}{4 \ell}\)
\(\sqrt{\frac{T}{T+16}}=\frac{1}{3}\)
\(\frac{T}{T+16}=\frac{1}{9}\)
\(9 \mathrm{T}=\mathrm{T}+16 \quad \therefore 8 \mathrm{T}=16 \quad \therefore \mathrm{T}=2 \mathrm{~N}\)
\(\sqrt{\frac{T}{T+16}}=\frac{1}{3}\)
\(\frac{T}{T+16}=\frac{1}{9}\)
\(9 \mathrm{T}=\mathrm{T}+16 \quad \therefore 8 \mathrm{T}=16 \quad \therefore \mathrm{T}=2 \mathrm{~N}\)
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
- A vessel is filled with two different liquids which do not mix. One is 40 cm deep and has refractive index 1.6 and other is 30 cm deep and has refractive index 1.5. The apparent depth of vessel when viewed normally isMHT CET 2024 Medium
- Out of the following musical instruments, which is 'NOT' a percussion instrument?MHT CET 2024 Easy
- Out of the fundamental forces in nature, maximum and minimum range is respectively forMHT CET 2020 Easy
- Two parallel wires of equal lengths are separated by a distance of \(3 \mathrm{~m}\) from each other. The currents flowing through \(1^{\text {st }}\) and \(2^{\text {nd }}\) wire is \(3 \mathrm{~A}\) and \(4.5 \mathrm{~A}\) respectively in opposite directions. The resultant magnetic field at mid point between the wires \(\left(\mu_0=\right.\) permeability of free space)MHT CET 2023 Hard
- An object is located on a wall, its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens in placed at a distance ' \(\mathrm{d}\) ' in front of the second wall. The required focal length of the lens isMHT CET 2021 Medium
- A train has to negotiate a curve of radius 'r' \(\mathrm{m}\), the distance between the rails is \({ }^{\prime}{ }^{\prime} \mathrm{m}\) and outer rail is raised above inner rail by distance of ' \(\mathrm{h}^{\prime} \mathrm{m}\). If the angle of banking is small, the safety speed limit on this banked road isMHT CET 2020 Easy
More PYQs from MHT CET
- \(\int \frac{\log \sqrt{x}}{3 x} \mathrm{~d} x\) is equal toMHT CET 2024 Easy
- Which among the following compounds in used I Swartz reaction?MHT CET 2022 Easy
- Let the speed of light and the polarising angle for a given medium be ' \(V\) ' and ' \(\mathrm{i}_p\) ' respectively. The relation between them is ( \(C=\) speed of light in vacuum)MHT CET 2025 Medium
- Two bodies 'A' an 'B' start from the same point at the same instant and move along a straight line. Body 'A' moves with uniform acceleration ' \(a\) ' and body ' \(B\) ' moves with uniform velocity ' \(V\) '. They meet after time ' \(t\) '. The value of ' \(t\) ' isMHT CET 2023 Easy
- If \(x^2+y^2=\mathrm{t}+\frac{1}{\mathrm{t}}\) and \(x^4+y^4=\mathrm{t}^2+\frac{1}{\mathrm{t}^2}\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) is equal toMHT CET 2023 Medium
- Brown ring test is used for the detection of which radical?MHT CET 2016 Easy