# A wooden cube (density of wood d) of side l floats in a liquid of density ρ with its upper and lower surfaces horizontal….

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 l2 x g

Since , F = -kx

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

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

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