Direct Link: http://i.imgur.com/4YZTUVS.png Please make sure to explain A solid

Question

Direct Link: http://i.imgur.com/4YZTUVS.png

Please make sure to explain

A solid sphere of mass floats in a beaker of water as shown. A second sphere of the same material but of mass 2mis placed in a second beaker of water. In the space provided, sketch the final position of the second sphere. In its final position, how does the buoyant force on the larger sphere compare to its weight? How does the volume displaced by the larger sphere compare to that displaced by the smaller sphere? Are your answers to questions a and b consistent with Archimedes' principle? Explain.

Explanation / Answer

Answer

c)_ Archimedes principle is applicable both question A)& B)

Archimedes principle is that upward buoyant force that is exerted on a body immersed in a fluid , whether fully or partially submerged is equal to wt. of the fluid that the body displaces.

Archimedes principle allows the buoyancy of an object partially or wholly immersed in a liquid to be calculated. The downward force on the object is simply its weight. The upward, or buoyant, force on the object is that stated by Archimedes' principle, above. Thus the net upward force on the object is the difference between the buoyant force and its weight. If this net force is positive, the object rises; if negative, the object sinks; and if zero, the object is neutrally buoyant - that is, it remains in place without either rising or sinking.

Wt. of the second sphere = 2mg

g= acceleration due to gravity=9.8m/s2

2m=mass of the sphere

Wt. of the water,w= mass of water * acceleration due to gravity

So, mass of the water =density* volume

Suppose, density of water =1gm/cc

Vol.of the sphere = (4/3)(22/7)r^3 , does not depend on the mass.

So, vol=(mass/density)

Larger sphere vol.=2m(density of water, d=1gm/cc)

Smaller sphere volume=m

Volume ratio=2:1

MASS-2M-SPHER DIAGRAM

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