enEnglishguગુજરાતી
JEE Mains · Physics · STD 11 - 13. oscillations
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
- A \(\frac{1}{2}\)
- B \(\frac{1}{{30}}\ln \,3\)
- C \(2\)
- D \(\frac{1}{{15}}\ln \,3\)
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 \(\frac{b}{m}=\frac{1}{15} \ell \mathrm{n} 3\)
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
- Match List - I with List - II.
List - I List - II (A) Young’s Modulus (I) \(M L^{-1} T^{-1}\) (B) Torque (II) \(M L^{-1} T^{-2}\) (C) Coefficient of Viscosity (III) \(M^{-1} L^3 T^{-2}\) (D) Gravitational Constant (IV) \(M L^2 T^{-2}\)
Choose the correct answer from the options given below :JEE Mains 2025 Medium - A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(x -\) axis. Identify all figures that correctly represent the motion qualitatively. (\(a =\) acceleration, \(v =\) velocity, \(x =\) displacement, \(t =\) time)
JEE Mains 2019 Hard - The \(P-V\) diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process \(CD\) is (use \(\gamma=1.4\)) (in \(J\))
JEE Mains 2021 Medium - A conducting circular loop of area \( 1.0 m^{2} \) is placed perpendicular to a magnetic field which varies as \( B = \sin(100 t) \) Tesla. If the resistance of the loop is 100 \( \Omega \), then the average thermal energy dissipated in the loop in one period is ___________ J.JEE Mains 2026 Medium
- A spring stretches by \(2\) mm when it is loaded with a mass of \(200\) g. From equilibrium position the mass is further pulled down by \(2\) mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g \(= 10\) m/s\(^2\))JEE Mains 2026 Hard
- A metallic rod oflength '\(l\)' is tied to a string oflength \(2l\). and made to rotate with angular speed w on a horizontal table with one end of the string fixed. Ifthere is a vertical magnetic field '\(B\)' in the region, the \(e.m.f.\) induced across the ends of the rod is
JEE Mains 2013 Medium
More PYQs from JEE Mains
- The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is \(\frac{4}{3}\).The wavelength of the same light when it is passing through a transparent medium having refractive index of \(\frac{3}{2}\) is __________ nm.JEE Mains 2026 Easy
- Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_A\) and \(\lambda_B\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.JEE Mains 2023 Easy
- A man of \(60\,kg\) is running on the road and suddenly jumps into a stationary trolly car of mass \(120\,kg\). Then. the trolly car starts moving with velocity \(2\,ms ^{-1}\). The velocity of the running man was _________\(ms ^{-1}\). when he jumps into the carJEE Mains 2022 Medium
- Let the line passing through the points, \(P(2,-1,2)\) and \(Q(5,3,4)\) meet the plane \(x-y+z=4\) at the point \(R\). Then the distance of the point \(R\) from the plane \(x+2 y+3 z+2=0\) measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal toJEE Mains 2023 Hard
- A rod of length \(50\,cm\) is pivoted at one end. It is raised such that if makes an angle of \(30^o\) fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in \(rad\,s^{-1}\) ) will be \((g = 10\,ms^{-2})\)
JEE Mains 2019 Medium - In the given electromagnetic wave \(E_y=600 \sin (\omega t-k x) \mathrm{Vm}^{-1}\), intensity of the associated light beam is what? (in \(\mathrm{W} / \mathrm{m}^2\) ); (Given \(\epsilon_0=\) \(\left.9 \times 10^{-12} \mathrm{C}^{-2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)\)JEE Mains 2024 Hard