#1 Bowling balls can be made from a variety of substances and are required to ha

Question

#1 Bowling balls can be made from a variety of substances and are required to have a circumference of roughly 27.4 inches. The construction of the ball typically consists of a high density core surrounded by a lower density shell. Suppose a bowling ball floats in water with half of its volume submerged. If the specific gravity of the shell is 0.350 and the specific gravity of the core is 0.560, calculate the thickness of the shell.

*I thought it would be 0.44 but it's wrong* *hint Apply Newton's second law with two forces acting on the system – gravity and buoyancy.*

Explanation / Answer

Here ,

let the thickness of shell is t

Now outer radius of shell . r = 27.4/(2 *pi)

r = 27.4/(2 * pi)

r = 4.36 inch

Now , for the shell to half submerged

(2/3) * 3.141 * (4.36)^3 * 1 = (4/3) * 3.141 *((4.36^3 - (4.36 - t)^3)*0.56 + (4.36 - t)^3)

solving for t

t = 1.49 inch

the thickness of shell is 1.49 inch

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