A pendulum with time period of \(1\, s\) is losing energy due to damping. At certain time its energy is \(45\, J\). If after completing \(15\,oscillations\) , its energy has become \(15\, J\), its damping constant (in \(s^{-1}\) ) is

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{{15}}\ln \,3\)

Step-by-step Solution

Detailed explanation

As we know, \(E=E_{0} e^{-\frac{b t}{m}}\)

\(15=45 e^{-\frac{b 15}{m}}\)

[As no. of oscillations \(=15 \text { so } t=15 \mathrm{sec}]\)

\(\frac{1}{3}=e^{-\frac{b 15}{m}}\)

Taking log on both sides

\(\frac{b}{m}=\frac{1}{15} \ell \mathrm{n} 3\)

Same subject

What will be the nature of flow of water from a circular tap, when its flow rate increased from \(0.18\, L / min\) to \(0.48\, L / min\) ? The radius of the tap and viscosity of water are \(0.5\, cm\) and \(10^{-3}\, Pa s\), respectively. (Density of water : \(10^{3}\, kg / m ^{3}\) )

JEE Mains 2021 Medium
A parallel plate capacitor has plate area \(40\,cm ^2\) and plates separation \(2\,mm\). The space between the plates is filled with a dielectric medium of a thickness \(1\,mm\) and dielectric constant \(5\) . The capacitance of the system is :

JEE Mains 2023 Medium
Given below are two statements: Statement \(I:\) If heat is added to a system, its temperature must increase. Statement \(II:\) If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below

JEE Mains 2023 Medium
Four identical discs each of mass ' \(M\) ' and diameter ' \(a\) ' are arranged in a small plane as shown in figure. If the moment of inertia of the system about \(OO ^{\prime}\) is \(\frac{ x }{4} Ma ^{2}\). Then, the value of \(x\) will be \(......\)

JEE Mains 2022 Medium
A metal wire of length \(0.5 m\) and cross-sectional area \(10^{-4}\; m ^{2}\) has breaking stress \(5 \times 10^{8}\; Nm ^{-2}\). A block of \(10\; kg\) is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be \(ms ^{-1}\).

JEE Mains 2022 Hard
The recoil speed of a hydrogen atom after it emits a photon in going from \(n =5\) state to \(n =1\) state will be ..... \(m/s\)

JEE Mains 2021 Hard

Explore more questions on app

From JEE Mains

A mixture of carbon dioxide and oxygen has volume \(8310\) cm\(^3\), temperature \(300\) K, pressure \(100\) kPa and mass \(13.2\) g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _______.
(Assume both carbon dioxide and oxygen gases behave like ideal gases) \([R = 8.31\) J/mol.K\(]\)

JEE Mains 2026 Hard
In a Young's double slit experiment, light of \(500\, nm\) is used to produce an interference pattern. When the distance between the slits is \(0.05\, mm\), the angular width (in degree) of the fringes formed on the distance screen is close to\(........^o\)

JEE Mains 2020 Medium
A \(5\) mg particle carrying a charge of \(5\pi\times 10^{-6}\) C is moving with velocity of \((3\hat{i}+2\hat{k})\times 10^{-2}\) m/s in a region having magnetic field \(\vec{B} = 0.1\hat{k}\) Wb/m\(^2\). It moves a distance of \(\alpha\) meter along \(\hat{k}\) when it completes \(5\) revolutions. The value of \(\alpha\) is ________.

JEE Mains 2026 Hard
A rubber ball is released from a height of \(5\, m\) above the floor. It bounces back repeatedly, always rising to \(\frac{81}{100}\) of the height through which it falls. Find the average speed of the ball. (Take \(g =10 ms ^{-2}\) ) (in \(ms ^{-1}\))

JEE Mains 2021 Hard

Explore more questions on app