Question

Two cylinders with the same mass density rC = 713 kg / m3 are floating in a container of water (with mass density rW = 1025 kg / m3). Cylinder #1 has a length of L1 = 20 cm and radius r1 = 5 cm. Cylinder #2 has a length of L2 = 10 cm and radius r2 = 10 cm. If h1 and h2 are the heights that these cylinders stick out above the water, what is the ratio of the height of Cylinder #2 above the water to the height of Cylinder #1 above the water (h2 / h1)?

Answer 1

Answer:

$\dfrac{h_2}{h_1}=\dfrac{1}{2}$

Explanation:

Lets take h is height of cylinder immersed in the water

We know that for floating body

$h=\dfrac{\rho_cL}{\rho_l}$

Where $\rho_c$ density of cylinder

$\rho_l$ density of water

For both cylinder fluid is same also density of cylinders are also same

So

$\dfrac{h_1}{L_1}=\dfrac{h_2}{L_2}$

$\dfrac{h_1}{h_2}=\dfrac{L_1}{L_2}$

$\dfrac{h_1}{h_2}=\dfrac{20}{10}$

$\dfrac{h_2}{h_1}=\dfrac{1}{2}$