Question

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 0.800, calculate the thickness of the shell.

Answer 1

First of all let's do the numerical parts:

Given that:

Circumference of ball, P = 27.4 in = 69.596 cm

Therefore, Radius of the ball is given by:

Hence, Total volume of the ball is given by:

Density of core, = 0.800 x 1000 kg/m³ = 800 kg/m³

Density of shell, = 0.350 x 1000 kg/m³ = 350 kg/m³

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>​​​​​​​

(Let's forget about the units in this part for convenience)

Given that half of the volume is in water.

Therefore, mass of the water displaced = (Volume x density) = V/2 x 1000= 500 V

During floating, Mass of ball = mass of the water displaced

Therefore, Mass of ball = m = 500 V

Total mass of ball is given by:

Let V_cbe the volume of the shell.

Substituting all values:

Therefore, Radius of the core is given by:

​​​​​​​

Therefore, Thickness of shell is given by: