There is a cylindrical bottle of negligible mass and radius 2.5 cm floating in the water of density 103 kg m- 3 filled with 310 ml of water inside it. Now the bottle is slightly dipped into water and released. The frequency of oscillation is

Question

There is a cylindrical bottle of negligible mass and radius 2.5 cm floating in the water of density 103 kg m- 3 filled with 310 ml of water inside it. Now the bottle is slightly dipped into water and released. The frequency of oscillation is (A) 3.75 s- 1  (B) 1.25 s- 1  (C) 2.75 s- 1  (D) 3.00 s- 1

Tardigrade Admin · Accepted Answer

Let at equilibrium, y length of the bottle is immersed in water:- So, mg=fb u o mg=ρ (A y)g ..... (.1.) [Equilibrium Condition] Now it is further pushed by distance â²xâ² Fr e s t o r i n g=ρ [.Ax + y .]g-mg mω 2x=ρ Axg+ρ Ayg-mg ω =√(ρ A g/m)=√(ρ A g/ρ V)=√(π r2 g/V)=2π f ∴ f=(1/2 π )√(π r2 g/V)=1.25 s- 1

Q. There is a cylindrical bottle of negligible mass and radius $2.5 c m$ floating in the water of density $1 0^{3} k g m^{- 3}$ filled with $310 m l$ of water inside it. Now the bottle is slightly dipped into water and released. The frequency of oscillation is

$3.75 s^{- 1}$

$1.25 s^{- 1}$

$2.75 s^{- 1}$

$3.00 s^{- 1}$

Q. There is a cylindrical bottle of negligible mass and radius 2.5cm floating in the water of density 103kgm−3 filled with 310ml of water inside it. Now the bottle is slightly dipped into water and released. The frequency of oscillation is

3.75s−1

1.25s−1

2.75s−1

3.00s−1

Q. There is a cylindrical bottle of negligible mass and radius $2.5 c m$ floating in the water of density $1 0^{3} k g m^{- 3}$ filled with $310 m l$ of water inside it. Now the bottle is slightly dipped into water and released. The frequency of oscillation is

$3.75 s^{- 1}$

$1.25 s^{- 1}$

$2.75 s^{- 1}$

$3.00 s^{- 1}$