First slide

Simple hormonic motion

Question

A cubical body of density $σ$ , side L floats in a liquid of density $ρ$ ( $(ρ < σ)$ . If it is slightly displaced downwards and released, the time period will be

Difficult

A

$2 π \sqrt{\frac{ρ L}{σ g}}$
B

$2 π \sqrt{\frac{ρ g}{σ L}}$
C

$2 π \sqrt{\frac{σ L}{ρ g}}$
D

$2 π \sqrt{\frac{σ g}{ρ L}}$

Solution

$w h e n i t i s d i s p l a c e d a l i t t l e b y y e x t r a b u o y a n t f o r c e d e v e l o p e d i s A y ρ g w h e r e A i s a r e a o f c r o s s s e c t i o n F = - A y g ρ = m a a = - \frac{A y g ρ}{m} = \frac{A y g ρ}{A L σ} = - \frac{g ρ}{L σ} y = - ω^{2} y ω = \sqrt{\frac{g ρ}{L σ}} T = 2 π \sqrt{\frac{L σ}{ρ g}}$

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