A ping pong ball has a mass of 2.47 g,a diameter of 4.0 cm and is made of celluloid.( )Find the thickness of the celluloid.
A)0.017 cm
B)0.034 cm
C)0.051 cm
D)0.42 cm

Question

A ping pong ball has a mass of 2.47 g,a diameter of 4.0 cm and is made of celluloid.(  )Find the thickness of the celluloid.
A)0.017 cm 
B)0.034 cm 
C)0.051 cm 
D)0.42 cm

Quizplus · Accepted Answer

The volume of the ping pong ball can be calculated as:
V = (4/3)πr^3
r = d/2 = 2.0 cm = 0.02 m
V = (4/3)π(0.02)^3 = 3.35×10^-6 m^3

The density of celluloid is approximately 1.4 g/cm^3 or 1400 kg/m^3.
So, the mass of the celluloid material in the ping pong ball can be calculated as:
m = ρV = 1400 × 3.35×10^-6 = 0.00469 kg

The thickness of the celluloid can be calculated using the formula for the volume of a spherical shell:
V = (4/3)π[(R^3) - (r^3)]
where R is the outer radius of the shell and r is the inner radius (which is equal to the radius of the ping pong ball).

R = r + thickness
The mass of the celluloid material in the shell can be calculated as:
m_shell = ρV
m_shell = ρ[(4/3)π(R^3 - r^3)]
m_shell = ρ[(4/3)π((r + thickness)^3 - r^3)]

The total mass of the ping pong ball and the celluloid shell is equal to the mass of the ping pong ball (since the celluloid is very thin in comparison). So we can set the two equations equal and solve for thickness.

m_shell + m = m_pingpongball
ρ[(4/3)π((r + thickness)^3 - r^3)] + 0.00469 = 0.00247

Simplify the equation and solve for thickness:
thickness = 0.034 cm.

So, the correct answer is B) 0.034 cm.

A Ping Pong Ball Has a Mass of 2