A bottle weighing 220 g and of area of cross-section 50 cm2, and height 4 cm oscillates on the surface of water in vertical position. Its frequency of oscillation is

Question

A bottle weighing 220 g and of area of cross-section 50 cm2, and height 4 cm oscillates on the surface of water in vertical position. Its frequency of oscillation is (A) 1.5 Hz (B) 2.5 Hz (C) 3.5 Hz (D) 4.5 Hz

Tardigrade Admin · Accepted Answer

Let h be the depth of bottle in water then Ahρ g = mg or h =(m/Aρ)=(200/50×1)=4 cm. Now time period, T=2π√(h/g) or upsilon=(1/T)=(1/2π)√(g/h) =(7/2×22) √(980/4)=2.5 Hz

Q. A bottle weighing $220 g$ and of area of cross-section $50 c m^{2}$ , and height $4 c m$ oscillates on the surface of water in vertical position. Its frequency of oscillation is

1.5 Hz

2.5 Hz

3.5 Hz

4.5 Hz

Let h be the depth of bottle in water then
$A h ρ g = m g or h = \frac{m}{A ρ} = \frac{200}{50 \times 1} = 4 c m .$
Now time period,
$T = 2 π \frac{h}{g} or υ = \frac{1}{T} = \frac{1}{2 π} \frac{g}{h}$
$= \frac{7}{2 \times 22} \frac{980}{4} = 2.5$ Hz

Q. A bottle weighing 220g and of area of cross-section 50cm2, and height 4cm oscillates on the surface of water in vertical position. Its frequency of oscillation is