MHT CET · Physics · Waves and Sound
A uniform metal wire has length 'L', mass 'M' and density ' \(\mathrm{Q}\) '. It is under tension 'T"
and ' \(v^{\prime}\) is the speed of transverse wave along the wire. The area of cross-section of
the wire is
- A \(\frac{\mathrm{v}^{2} \varrho}{\mathrm{T}}\)
- B \(\frac{\mathrm{T}}{\mathrm{v}^{2} \varrho}\)
- C \(\mathrm{T}^{2} \varrho \mathrm{v}\)
- D \(\mathrm{Tv}^{2} \varrho\)
Answer & Solution
Correct Answer
(B) \(\frac{\mathrm{T}}{\mathrm{v}^{2} \varrho}\)
Step-by-step Solution
Detailed explanation
\((\mathrm{C})\)
\(\begin{aligned} \mathrm{V} &=\sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \end{aligned}\left[\mathrm{m}=\frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{AL} \rho}{\mathrm{L}}=\mathrm{A\rho}\right]\)
\(\therefore \mathrm{V}=\sqrt{\frac{\mathrm{T}}{\mathrm{A} \rho}}\)
\(\therefore \mathrm{V}^{2}=\frac{\mathrm{T}}{\mathrm{A} \rho}\)
\(\mathrm{A}=\frac{\mathrm{T}}{\mathrm{V}^{2} \rho}\)
\(\begin{aligned} \mathrm{V} &=\sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \end{aligned}\left[\mathrm{m}=\frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{AL} \rho}{\mathrm{L}}=\mathrm{A\rho}\right]\)
\(\therefore \mathrm{V}=\sqrt{\frac{\mathrm{T}}{\mathrm{A} \rho}}\)
\(\therefore \mathrm{V}^{2}=\frac{\mathrm{T}}{\mathrm{A} \rho}\)
\(\mathrm{A}=\frac{\mathrm{T}}{\mathrm{V}^{2} \rho}\)
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
- For a common emitter configuration, if ' \(\alpha\) ' and ' \(\beta\) ' have their usual meanings, the incorrect relation between ' \(\alpha\) ' and ' \(\beta\) ' isMHT CET 2023 Medium
- A lead sphere of mass ' \(m\) ' falls in viscous liquid with terminal velocity \(\mathrm{V}_0\). Another lead sphere of mass ' 8 m ' but of same material will fall through the same liquid with terminal velocityMHT CET 2024 Medium
- Two capacitors of \(100 \mu \mathrm{~F}\) and \(50 \mu \mathrm{~F}\) are connected in parallel. If the potential difference across \(100 \mu \mathrm{~F}\) is 20 V and across \(50 \mu \mathrm{~F}\) is 40 V , then the common potential of the parallel combination will be (same polarities of the capacitor connected together)MHT CET 2025 Medium
- From Brewster's law, except for polished metallic surface, the polarising angleMHT CET 2016 Easy
- A needle is \(7 \mathrm{~cm}\) long. Assuming that the needle is not wetted by water, what is the weight of the needle, so that floats on water?
\(\left[\mathrm{T}=\text { surface tension of water }=70 \frac{\mathrm{dyne}}{\mathrm{cm}}\right]\) [acceleration due to gravity \(=980 \mathrm{~cm} \mathrm{~s}^{-2}\) ]MHT CET 2021 Easy - White light consists of wavelengths range from \(480 \mathrm{~nm}\) to \(672 \mathrm{~nm}\). What will be the wavelength range when white light is passed through glass of refractive index 1.6?MHT CET 2021 Easy
More PYQs from MHT CET
- A monoatomic ideal gas, initially at temperature \(T_1\) is enclosed in a cylinder fitted with frictionless piston. The gas is allowed to expand adiabatically to a temperature \(\mathrm{T}_2\) by releasing the piston suddenly. \(L_1\) and \(L_2\) are the lengths of the gas columns before and after the expansion respectively. The ratio \(T_2 / T_1\) isMHT CET 2024 Hard
- Hyperconjugation is not observed inMHT CET 2022 Medium
- Primary lesion called chancre at the site of infection, is a characteristic symptom of _________ diseaseMHT CET 2024 Medium
- If \(y=3 \cos (\log x)+4 \sin (\log x)\), then \(x^2 y_2+x y_1=\)MHT CET 2022 Easy
- A double convex lens made of glass has both radii of curvature of magnitude \(20 \mathrm{~cm}\). Incident light rays parallel to the axis of the lens will converge to a point at a distance ' \(L\) ' from the common pole P. The value of L is [Refractive index of glass \(=1.5\) ]MHT CET 2022 Medium
- For the differential equation \(\left[1-\left(\frac{d y}{d x}\right)^2\right]^{5 / 2}=8 \frac{d^2 y}{d x^2}\) has the order and degreeMHT CET 2022 Easy