Q: A wooden cube (density of wood d) of side *l* floats in a liquid of density ρ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period T. Then, T is equal to

(a) $\displaystyle 2\pi \sqrt{\frac{l\rho}{(\rho-d)g}} $

(b) $\displaystyle 2\pi \sqrt{\frac{l d}{\rho g}} $

(c) $ \displaystyle 2\pi \sqrt{\frac{l\rho}{d g}} $

(d) $ \displaystyle 2\pi \sqrt{\frac{l d}{(\rho-d)g}} $

Ans: (b)

Sol: F= -ρ l^{2 }*x *g

Since , F = -kx

$\displaystyle T = 2\pi \sqrt{\frac{m}{k}} $

$ \displaystyle T = 2\pi \sqrt{\frac{l^3 d}{\rho l^2 g}} $

$ \displaystyle T = 2\pi \sqrt{\frac{l d}{\rho g}} $