Question

Bowling balls can be made from a variety of substances and are required to have a circumference of roughly 27.0 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.

Answer 1

circumference = 2*pi*R = 27 inches = (27*0.0254) m = 0.6858 m

R = 0.11 m

Volume of core V1= (4/3)*pi*r^3

volume of the shell V2= (4/3)*pi*(R^3 - r^3)

volume of the ball = V = (4/3)*pi*R^3

buoyancy force = weight of the ball

dw*V/2*g = dc*V1*g + ds*V2*g

dw*V/2 = dc*v1 + ds*v2

dw*(4/3)*pi*R^3 = 2*dc*(4/3)*pi*r^3 + 2*ds*(4/3)*pi*(R^3 - r^3)

dw*R^3 = 2*dc*r^3 + 2*ds*(R^3 - r^3)

dw*R^3 = 2*r^3*(dc-ds) + 2*ds*R^3

R^3*(dw - 2ds) = 2*r^3*(dc-ds)

0.11^3*(1000-(2*350)) = 2*r^3*(560-350)

r = 0.09833 m

t = R-r = 0.11-0.09833 m = 0.01167 m = 0.46 inches ,---answer