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Classical Mechanics

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Weight to Keep a Helium Balloon from Floating Away

CLMECH-JETEJN

Lily bought a helium-filled balloon for her birthday party. The balloon is a sphere of a radius of $45 \space cm$. The mass of the latex material the balloon is made of is $11 \space g$. Lily made several weights to hold the balloon down. Each weight has a mass of $0.12 \space kg$ and a volume of $0.046 \space m^3$.

What is the minimum number of weights that Lily should attach to the balloon so that it does not float to the ceiling in her room? Assume normal temperature and pressure. The density of air is $1.2 \space kg/m^3$ and the density of helium is $0.16 \space kg/m^3$.