MHT CET · Physics · Oscillations
A particle is suspended from a vertical spring which is executing S.H.M. of frequency \(5 \mathrm{~Hz}\). The spring is unstretched at the highest point of oscillation. Maximum speed of the particle is \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)\)
- A \(\frac{1}{\pi} \mathrm{m} / \mathrm{s}\)
- B \(\frac{1}{4 \pi} \mathrm{m} / \mathrm{s}\)
- C \(\frac{1}{2 \pi} \mathrm{m} / \mathrm{s}\)
- D \(\pi \mathrm{m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\pi} \mathrm{m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
Amplitude of SHM, A \(=\frac{\mathrm{mg}}{\mathrm{k}}=\frac{\mathrm{g}}{\omega^2}\)
\(\omega=2 \pi \mathrm{f}=2 \pi \times 5=10 \pi\)
\(\begin{aligned} & \therefore \mathrm{A}=\frac{10}{100 \pi^2}=\frac{1}{10 \pi^2} \\ & \mathrm{~V}_{\max }=\mathrm{A} \omega=\frac{1}{10 \pi^2} \times 10 \pi=\frac{1}{\pi} \mathrm{m} / \mathrm{s}\end{aligned}\)
\(\omega=2 \pi \mathrm{f}=2 \pi \times 5=10 \pi\)
\(\begin{aligned} & \therefore \mathrm{A}=\frac{10}{100 \pi^2}=\frac{1}{10 \pi^2} \\ & \mathrm{~V}_{\max }=\mathrm{A} \omega=\frac{1}{10 \pi^2} \times 10 \pi=\frac{1}{\pi} \mathrm{m} / \mathrm{s}\end{aligned}\)
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 body performing uniform circular motion of radius ' \(R\) ' has frequency ' \(n\) '. Its centripetal acceleration isMHT CET 2020 Medium
- Which of the following is the dimensional formula for electric polarisation?MHT CET 2019 Easy
- The \(\mathrm{P}-\mathrm{V}\) diagrams for particular gas of different thermodynamic processes are given by
MHT CET 2024 Easy - An electron(e) is revolving in a circular orbit of radius 'r' in hydrogen atom. The angular momentum of the electron is (M = magnetic dipole moment associated with it and \(\mathrm{m}=\) mass of electron \()\)MHT CET 2020 Medium
- If only \(5 \%\) of the total current is to be passed through galvanometer of resistance G, then the resistance of the shunt will beMHT CET 2025 Easy
- If a unit positive charge is shifted from a region of low potential to a region of high potential, then the electric potential energy of the systemMHT CET 2024 Easy
More PYQs from MHT CET
- What is the self inductance of a coil in which an induced emf of \(2 \mathrm{~V}\) is set up, when the current is changing at the rate of \(4 \mathrm{As}^{-1}\)MHT CET 2012 Medium
- The area bounded by the curve, \(y=-x^2\), x-axis, \(x=1\) and \(x=4\), isMHT CET 2022 Easy
- Three equal charges \(q_1, q_2\) and \(q_3\) are placed on the three corners of a square of side \(a\). If the force between \(q_1\) and \(q_2\) is \(F_{12}\) and that between \(q_1\) and \(q_3\) is \(F_{13}\), then the ratio of magnitudes \(\left(\frac{F_{12}}{F_{13}}\right)\) isMHT CET 2022 Medium
- Identify the reagent involved in Sandmeyer reaction.MHT CET 2025 Easy
- What is the change in oxidation number of nitrogen in following conversion?
\( \mathrm{NO}_3^{-} \longrightarrow \mathrm{NO}_2 \)MHT CET 2021 Medium - Carborundum isMHT CET 2007 Medium