Verified Solution • 2025–26 Session moderate

QJEEM19Phed07: JEE Main 2019 Physics - Class 11 JEEM19Phed07 Solution: A cylindrical plastic bottle of negligible mass is filled with…

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 = 103 kg/m3).

Multiple Choice Options

  • A 2.50 rad s−1
  • B 3.75 rad s−1
  • C 5.00 rad s−1
  • D 7.90 rad s−1

Step-by-Step Verified Solution

Restoring force due to pressing the bottle with small amount x,

F = −(ρAx)g

⇒ ma = −(ρAx)g

⇒ a = −(ρAgm)x

∴ ω2=ρAgm = ρ(πr2)gm

⇒ ω = 103×π×(2.5×10−2)2×10310×10−3 = 7.90 rad/s

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