Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2014PhysicsOscillationsActual

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).

Options

  1. A231 s
  2. B142 s
  3. C208 s
  4. D161 s

Correct answer

D. 161 s

Step-by-step solution

A = A 0 e − b t 2 m b is related to viscosity 8 = 10 e − b a 40 2 m 5 = 10 e − b C o 2 t 2 m ln 5 4 ln 2 = 40 t × 1.3 t = 40 × ( ln 2 ) × 1.3 ln 5 − 2 ln 2 = 40 × 0.693 × 1.3 1.601 − 2 × 0.693 ≃ 161 sec

Practice Oscillations on Quantrex Academy →

More from Oscillations

A tank contains two immiscible liquids of densities 6 and 2 . The higher density liquid is filled up to a height L/2 from the bottom. A thin rod of density and length L is fully im 2026The frequency of oscillation of a mass m suspended by a spring is v₁ . If the length of the spring is cut to half, the same mass oscillates with frequency v₂ . The value of v₂/v₁ i 2026A 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 2026A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from x = A to x = A 2 is _______ sec. 2026Match List-I with List-II. List-I List-II A. ^2 t I. Periodic with time period T = but not simple harmonic motion (SHM) B. ^3(2 t) II. Periodic with time period T = 2 but Not SHM C 2026A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is ______. ( g is acceleration due to gra 2026The velocity of a particle executing simple harmonic motion along x -axis is described as v^2 = 50 - x^2 , where x represents displacement. If the time period of motion is x 7 s, t 2026The equation of motion of a particle is given by x = a (50t + 3 ) cm. The particle will come to rest at time t₁ and it will have zero acceleration at time t₂ . The t₁ and t₂ respec 2026 Full Oscillations list All JEE Main PYQs