MHT CET · Physics · Oscillations
A particle is performing S.H.M. about its mean position with an amplitude 'a' and periodic time ' T '. The speed of the particle when. its displacement from mean position' is \(\frac{\mathrm{a}}{3}\) will be
- A \(\frac{2 \pi \mathrm{a}}{\mathrm{T}}\)
- B \(\frac{4 \sqrt{2} \pi \mathrm{a}}{3 \mathrm{~T}}\)
- C \(\frac{4 \pi^2 a}{3 T}\)
- D \(\frac{\sqrt{3} \pi^2 a}{2 T}\)
Answer & Solution
Correct Answer
(B) \(\frac{4 \sqrt{2} \pi \mathrm{a}}{3 \mathrm{~T}}\)
Step-by-step Solution
Detailed explanation
The speed of a particle performing SHM at displacement ' \(x\) ' from the mean position is given by, \(V=\omega \sqrt{a^2-x^2}\)
\(\begin{aligned}
& V=\omega \sqrt{a^2-\left(\frac{a}{3}\right)^2} \\
& V=\omega \sqrt{\frac{8 a^2}{9}} \\
& V=\frac{2 \pi}{T} \times \frac{2 \sqrt{2}}{3} \times a \\
& V=\frac{4 \sqrt{2} \pi a}{3 T}
\end{aligned}\)
\(\begin{aligned}
& V=\omega \sqrt{a^2-\left(\frac{a}{3}\right)^2} \\
& V=\omega \sqrt{\frac{8 a^2}{9}} \\
& V=\frac{2 \pi}{T} \times \frac{2 \sqrt{2}}{3} \times a \\
& V=\frac{4 \sqrt{2} \pi a}{3 T}
\end{aligned}\)
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 bomb is dropped by an aero plane flying horizontally with a velocity \(200 \mathrm{~km} / \mathrm{hr}\) and at a height of \(980 \mathrm{~m}\). At the time of dropping a bomb, the distance of the aero plane from the target on the ground to hit directly is \(\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right.\) )MHT CET 2021 Easy
- How much energy is imparted to an electron so that its de-Broglie wavelength
reduces from \(10^{-10} \mathrm{~m}\) to \(0 \cdot 5 \times 10^{-10} \mathrm{~m} ?(\mathrm{E}=\) energy of electron \()\)MHT CET 2020 Medium - A magnetic dipole of magnetic moment \(\mathrm{M}\), is freely suspended in a magnetic field of induction \(B\). The minimum and maximum value of potential energy of the dipole, respectively areMHT CET 2021 Medium
- A molecule consists of two atoms each of mass ' \(\mathrm{m}^{\prime}\) and separated by a distance ' \(\mathrm{d}^{\prime}\). At room temperature the average rotational kinetic energy is 'E', then its angular frequency isMHT CET 2020 Medium
- A particle of mass ' \(\mathrm{m}\) ' is rotating along a circular path of radius ' \(r\) ' having angular momentum ' \(L\) '. The centripetal force acting on the particle is given byMHT CET 2023 Medium
- A mass ' \(M\) ' is suspended by a rope from a rigid support at point ' \(P\) ' as shown in figure. Another rope is tied at end 'Q' and pulled horizontally with a force ' \(F\) '. If the rope makes an angle ' \(\theta\) ' with vertical then the tension in the string ' PQ ' is
MHT CET 2025 Medium
More PYQs from MHT CET
- What is wavenumber of a radiation having wavelength \(0.25 \mu \mathrm{~m}\) ?MHT CET 2024 Easy
- An ideal gas \((\gamma=1.5)\) is expanded adiabatically. To reduce root mean square velocity of molecules two times, the gas should be expandedMHT CET 2024 Hard
- On closing an open organ pipe from one end, it is noticed that the frequency of third harmonic is \(50 \mathrm{~Hz}\) more than the fundamental frequency of vibration in open organ pipe. The fundamental frequency of open organ pipe isMHT CET 2020 Medium
- Select the correct statements about alveoli from the following.
i. Air sac of each tertiary bronchi shows 10 to 12 alveoli.
ii. Each alveolus is surrounded by a network of capillaries.
iii. They are lined by ciliated pseudostratified epithelium.
iv. They provide surface area for exchange of gases.
v. There are about 700 million alveoli in the lungsMHT CET 2024 Hard - What is the major product obtained when tert-butyl bromide is heated with silver fluoride?MHT CET 2024 Medium
- Dimensions of Gyromagnetic ratio areMHT CET 2019 Medium