Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020PhysicsOscillationsPractice

A U tube of the uniform bore of cross-sectional area A is set up vertically with open ends. A liquid of mass M and density d is poured into it. The liquid column will oscillate with a period

Options

  1. A2 π M g
  2. B2 π M A d g
  3. C2 π M A d g
  4. D2 π M 2 A d g

Correct answer

D. 2 π M 2 A d g

Step-by-step solution

T = 2 π L g Where L is the length of the liquid is one of the limbs. However, if L is taken to be the length of the liquid column, then the length of liquid in each limb is L 2 . ⇒ T = 2 π L 2 g ⇒ M = AL d ⇒ L = M Ad ⇒ T = 2 π M 2 Adg

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 NTA Abhyas JEE Main PYQs