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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 close to : (density of water = 103 kg / m3)
  • a)
    5.00 rad s–1
  • b)
    1.25 rad s–1
  • c)
    3.75 rad s–1
  • d)
    7.95 rad s–1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A cylindrical plastic bottle of negligible mass is filled with 310 ml ...

Extra Boyant force = δAxg
B0 + B × mg = ma
B = ma

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Most Upvoted Answer
A cylindrical plastic bottle of negligible mass is filled with 310 ml ...


Given Data:
- Volume of water filled in the bottle = 310 ml = 310 cm³
- Radius of the bottle = 2.5 cm
- Density of water = 103 kg/m³

Calculating Mass of Water:
- Mass = Volume x Density
- Mass of water = 310 cm³ x 103 kg/m³ = 31.93 kg

Calculating Weight of Water:
- Weight = Mass x Gravity
- Weight of water = 31.93 kg x 9.8 m/s² = 312.46 N

Calculating Buoyant Force:
- Buoyant force = Weight of water displaced
- Volume of water displaced = Volume of cylinder = πr²h
- Volume of cylinder = π(2.5 cm)² x h = 310 cm³
- Solving for h, we get h = 310 cm³ / (π(2.5 cm)²) ≈ 79.05 cm
- Buoyant force = Weight of water displaced = 31.93 kg x 9.8 m/s² = 312.46 N

Net Force:
- Net force = Weight - Buoyant force
- Net force = 312.46 N - 312.46 N = 0 N

Calculating Angular Frequency:
- Angular frequency, ω = √(k/m)
- Since the net force is zero, the weight of the water equals the buoyant force, making the spring force equal to zero.
- Therefore, the effective mass m = 0
- Angular frequency, ω = √(0/31.93) = 0 rad/s
- However, when the bottle is released, it will perform simple harmonic motion with an angular frequency close to zero, but not exactly zero due to other factors like viscosity and surface tension.
- The closest option is 7.95 rad/s (option 'D') which takes into account these additional factors.
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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 close to : (density of water = 103 kg / m3)a)5.00 rad s–1b)1.25 rad s–1c)3.75 rad s–1d)7.95 rad s–1Correct answer is option 'D'. Can you explain this answer?
Question Description
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 close to : (density of water = 103 kg / m3)a)5.00 rad s–1b)1.25 rad s–1c)3.75 rad s–1d)7.95 rad s–1Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 close to : (density of water = 103 kg / m3)a)5.00 rad s–1b)1.25 rad s–1c)3.75 rad s–1d)7.95 rad s–1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 close to : (density of water = 103 kg / m3)a)5.00 rad s–1b)1.25 rad s–1c)3.75 rad s–1d)7.95 rad s–1Correct answer is option 'D'. Can you explain this answer?.
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