Q. A bottle weighing 220 g and of area of cross-section 50 cm$^{2}$ 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
Explanation
(b) Let $h$ be the depth of bottle in water then
$A\ h\ \rho\ g = mg\ \ or\ \ \ h = \frac{m}{A\rho} = \frac{200}{50 \times 1} = 4\ cm$
$T = 2\pi\sqrt{\frac{h}{g}}\ \ \ or\ \ \ v = \frac{1}{2} = \frac{1}{2\pi}\sqrt{\frac{g}{h}}$
$= \frac{7}{2 \times 22} = \sqrt{\frac{980}{4}} = 2.5\ Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.