Let at equilibrium, y length of bottle is immerged in water:
So, mg=fbuo
mg=ρ(Ay)g ..... (1) [Equilibrium Condition]
Now it is further pushed by distance x
Frestoring=ρ[A(x+y)]g−mg
mω2x=ρAxg+ρAyg−mg
ω=mρAg=ρVρAg=Vπr2g=7.9rad/sec
JEE Main 2019 — Physics Waves & Oscillations
A cylindrical plastic bottle of negligible mass is filled with 310ml 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 2.5cm then ω is close to: ( density of water =103kg/m3)
Held on 10 Jan 2019 · Verified 6 Jul 2026.
5.00 rad sec−1
2.50radsec−1
7.9radsec−1
3.75radsec−1
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