A hollow sphere of negligible mass and radius R is completely filled with a liquid so that its density is ρ.You now enlarge the sphere so its radius is 2R and completely fill it with the same liquid.What is the density of the enlarged sphere?
A)8 ρ
B)4 ρ
C)ρ/2
D)ρ
E)ρ/8

Question

Quizplus · Accepted Answer

Since the original sphere is completely filled with liquid of density ρ, the mass of the liquid inside the sphere is given by:

M = ρ * V

where V is the volume of the sphere. Using the formula for the volume of a sphere, we have:

V = (4/3) * π * R^3

So the mass of the liquid in the original sphere is:

M = (4/3) * π * R^3 * ρ

When the sphere is enlarged, the volume is increased by a factor of 8 (since the radius is doubled). However, the mass of the liquid inside the sphere is still the same, so the density must be reduced by a factor of 8:

ρ' = ρ / 8

So the density of the enlarged sphere is ρ/8 or answer choice E.

A Hollow Sphere of Negligible Mass and Radius R Is