MHT CET · Physics · Oscillations
A small mass 'm' is suspended at the end of a wire having (negligible mass) length 'L' and cross-sectional area 'A'. The frequency of oscillation for the S.H.M. along the vertical line is \((\mathrm{Y}=\) Young's modulus of the wire)
- A \(\frac{1}{2 \pi}\left(\frac{\mathrm{YA}}{\mathrm{mL}}\right)^{\frac{1}{2}}\)
- B \(\frac{2 \pi \mathrm{YA}}{\mathrm{mL}}\)
- C \(\frac{\mathrm{YA}}{2 \pi \mathrm{mI}}\)
- D \(2 \pi\left(\frac{\mathrm{YA}}{\mathrm{mL}}\right)^{\frac{1}{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2 \pi}\left(\frac{\mathrm{YA}}{\mathrm{mL}}\right)^{\frac{1}{2}}\)
Step-by-step Solution
Detailed explanation
If \(x\) is the extension of the wire then
\(P=\left(\frac{Y A}{L}\right) x \quad F=k x \quad \text { where } k=\frac{Y A}{L}\)
frequency of oscillation is given by
\(f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}=\frac{1}{2 \pi} \sqrt{\frac{Y A}{m L}}\)
\(P=\left(\frac{Y A}{L}\right) x \quad F=k x \quad \text { where } k=\frac{Y A}{L}\)
frequency of oscillation is given by
\(f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}=\frac{1}{2 \pi} \sqrt{\frac{Y A}{m L}}\)
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
- Light waves from two coherent sources arrive at two points on a screen with path difference of zero and \(\frac{\lambda^{\prime}}{2}\). The ratio of intensities at the points is \(\left(\cos 0^{\circ}=1, \cos \pi=-1\right)\)MHT CET 2023 Medium
- In the hysteresis curve the value of magnetization (B) which will be present in a substance when value of magnetizing force \((\mathrm{H})\) is made zero \((\mathrm{H}=0)\) is called asMHT CET 2023 Easy
- In Young's double slit experiment with monochromatic light of wavelength 600 nm, the distance between the slits is \(10^{-3} \mathrm{~m}\). For changing the fringe width by \(3 \times 10^{-5} \mathrm{~m}\)
a) the screen is moved away from the slit by 5 cm.
b) the screen is moved 5 cm towards the slits.
c) the screen is moved 3 cm towards the slits.
d) the screen is moved away from the slits by 3 cm.MHT CET 2025 Medium - Maximum kinetic energy gained by the charged particle in the cyclotron is independent ofMHT CET 2019 Medium
- A graph is plotted between the fringe-width (z) and the distance (D) between the slit and eye-piece, keeping other adjustment same. The correct graph is
MHT CET 2020 Easy - The resultant gate and its Boolean expression for the given circuit is
MHT CET 2020 Easy
More PYQs from MHT CET
- If \(\int \frac{5 \tan x}{\tan x-2} d x=x+a \log |\sin x-2 \cos x|+c\), then \(a\) (Where \(\mathrm{c}\) is constant of integration)MHT CET 2021 Hard
- Select the correct decreasing order of boiling points of compounds from the following.MHT CET 2025 Medium
- What is the molar mass of product hydrocarbon when 2 moles of methyl bromide reacts with large excess of sodium in dry ether?MHT CET 2024 Hard
- The standard reduction potential for \(\mathrm{Mg}^{2+} / \mathrm{Mg}\) is \(-2.37 \mathrm{~V}\) and for \(\mathrm{Cu}^{2+} / \mathrm{Cu}\) is \(0.337\). The \(E_{\text {cell }}^{\circ}\) for the following reaction is \(\mathrm{Mg}+\mathrm{Cu}^{2+} \longrightarrow \mathrm{Mg}^{2+}+\mathrm{Cu}\)MHT CET 2009 Easy
- Two identical parallel plate air capacitors are connected in series to a battery of e..m.f. \({ }^{\prime} \mathrm{V}^{\prime}\). If one of the capacitor is inserted in liquid of dielectric constant '\(\mathrm{K}^{\prime}\), then potential difference of the other capacitor will becomeMHT CET 2020 Medium
- What is bond angle \(\mathrm{F}-\mathrm{B}-\mathrm{F}\) in \(\mathrm{BF}_3\) ?MHT CET 2024 Medium