JEE Main 2019PhysicsOscillationsHardMCQ

JEE Main 2019 — Oscillations Question with Solution

JEE Main 2019 (10 Jan Shift 2)

Question

A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω. If the radius of the bottle is 2.5 cm then ω is close to: ( density of water =103kg/m3)

Choose an option

Show full solutionCorrect option: C
Correct answer
C7.9 rad sec-1⁡ 

Step-by-step explanation

Let at equilibrium, y length of bottle is immerged in water:

So, mg=fbuo

mg=ρAyg ..... (1) [Equilibrium Condition]

Now it is further pushed by distance x

Frestoring=ρ[Ax+y)g-mg

mω2x=ρAxg+ρAyg-mg

ω=ρAgm=ρAgρV=πr2gV=7.9 rad/sec

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About this question

This is a previous-year question from JEE Main 2019, covering the Oscillations chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.