a) A cube of wood whose edge is 12 mm is floating in a liquid in a glass with on

Question

a) A cube of wood whose edge is 12 mm is floating in a liquid in a glass with one of its faces parallel to the liquid surface. The density of wood is 909 kg/m^3, that of liquid is 1296 kg/m^3. How far hL below the liquid surface is the bottom face of the cube? b) A light oil is gently poured onto the immiscible liquid surface to form a 2.9 mm thick layer above the liquid. The density of the oil is 606 kg/m^3. When the wood cube attains hydrostatic equilibrium again, what will be the distance from the top of the liquid to the bottom face of the cube? c) Additional light oil is poured onto the liquid surface until the top surface of the oil coincides with the top surface of the wood cube (in hydrostatic equilibrium). How thick is the whole layer of the light oil?

Explanation / Answer

Let the cross-sectionalal area of wooden block be, A. Let it remain X mm above water surface while floating in equilibrium. Let its mass be M. and V be its volume. Law of floatation tells us Weight, therefore mass, too of wooden block = Weight therefore mass too of water displaced. So we have M = (12-X)x10^-3xAx1000; V = 12x10^-3xA, As we know M = Vxdensity or M = (12-x)A = 12xAx10^-3x900 or (12-x)/12 = 0.9 or 1 - x/12 = 0.9 or x/12 = 0.1 or x = 1.2 mm Similarly when 5 mm layer of oil is spread, let y mm be the distance of the top of cube from the top surface of liquid. Similar considerations tell us [12-(5-y)]x10^-3xAx1000+(5-y)x10^-3xAx… = 12x10^-3xAx900 or (7+y)+3-0.6 y = 10.8 or o.4 y = 0.8 or y = 2 mm So the distance of cube from top of liquid will be 2 mm To solve the third problem let the layer of liquid be Z mm thick. Similar consideration tell us [12-Z]x10^-3xAx1000+Zx10^-3xAx600 = 12x10^-3xAx900 or 12-Z+0.6Z=10.8 or 1.2 = 0.4Z or Z = 3 3 mm should be the thickness of the oil. I think the the sequence of second and third part of question has been exchanged. Third should have been asked first and then the second.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.