An empty rubber balloon has a mass of 12.5 g. The balloon is filled with helium at a density of 0.181 kg/m3. At this density the balloon has a radius of 0.498 m. If the filled balloon is fastened to a vertical line, what is the tension in the line? The density of air is 1.29 kg/m3.

5.5 N

Explanation:

mass of balloon (m) = 12.5 g = 0.0125 kg

density of helium = 0.181 kg/m^{3}

radius of the baloon (r) = 0.498 m

density of air = 1.29 kg/m^{3}

acceleration due to gravity (g) = 1.29 m/s^{2}

find the tension in the line

the tension in the line is the sum of all forces acting on the line

Tension = buoyant force + force by helium + force of weight of rubber

force = mass x acceleration

from density = / frac{mass}{volume}, mass = density x volume

buoyant force = density x volume x acceleration

where density is the density of air for the buoyant force

buoyant force = 1.29 x (/frac{4]{3} x π x 0.498^{3}) x 9.8 = 6.54 N

force by helium = density x volume x acceleration

force by helium = 0.181 x (/frac{4]{3} x π x 0.498^{3}) x 9.8 = 0.917 N

force of its weight = mass of rubber x acceleration

force of its weight = 0.0125 x 9.8 = 0.1225 N

Tension = buoyant force + force by helium + force of weight of rubber

the force of weight of rubber and of helium act downwards, so they

carry a negative sign.

Tension = 6.54 - 0.917 - 0.1225 = 5.5 N