A spherical shell of copper with an outer diameter of 18.0 cm floats on fresh wa

Question

A spherical shell of copper with an outer diameter of 18.0 cm floats on fresh water with two thirds its volume above the water's surface. Determine the inner diameter of the shell.

Question 2

A U-tube is filled with water until the liquid level is 28 cm above the bottom of the tube. An oil of specific gravity 0.74 is now poured into one arm of the U-tube until the level of the water in the other arm of the tube is 33 cm above the bottom of the tube. Find the level of the oil-water and oil-air interfaces in the other arm of the tube.
cm (oil-water)
cm (oil-air)

http://www.webassign.net/tipler6/13-p-088-alt.gif Picture for number 2

Explanation / Answer

Q1:

R1 = 18 cm =0.18 m

VOlume of displaced water = (2/3)(4/3)pi*R1^3

Volume of copper = (4/3)pi*R1^3 - (4/3)pi*R2^3

net Force along vertical direction is zero

Buyancy force = mCu*g

(2/3)(4/3)pi*R1^3*dw*g = dCu*g*((4/3)pi*R1^3 - (4/3)pi*R2^3)

(2/3)R1^3dW = dCu*(R1^3 - R2^3)

(2/3)*0.18^3*1000 = 8940*(0.18^3 -R2^3)

R2 = 0.175 m

R2 =17.54 cm

Q2: specific gravity to be the ratio of density as compared to water, which has a gravity of 1 water went up by 5cm, so this means that a weight equal to10cm worth of water was added to the other side.
as water doesn't really compress the water level on the other side of the arm must have dropped by 5cm, to counter the rise on the opposite side, this means its level is 28-5cm = 23 cm above the bottom. this is the water oil interface

as the weight of 10cm worth of water must have been added, and the oil is 0.74 the density of the water there must have been 10/0.74 = 13.514cm of oil added so the level of oil is 23+13.514 = 36.514 cm above the bottom. this is the oil air interface.

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