Volume of the plastic balloon = 15 m3
Density of hydrogen = 0.09 kg m-3
Mass of the unfilled balloon = 7.15 kg
Density of air = 1.3 kg m-3
(i) As we know,
Mass = volume of balloon x density of hydrogen
Substituting the value in the formula we get,
15 x 0.09 = 1.35 kg
Hence, mass of hydrogen in the balloon = 1.35 kg
(ii) Mass of hydrogen and balloon = mass of hydrogen in the balloon + mass of unfilled balloon = 7.15 + 1.35 = 8.5 kg
Hence, mass of hydrogen and balloon = 8.5 kg
(iii) Given,
mass of equipment = x kg
Hence,
Total mass of hydrogen, balloon and equipment = (8.5 + x) kg
(iv) Weight of the air displaced = upthrust = Volume of the balloon x density of the balloon x g
Hence,
Mass of the air displaced = volume of balloon x density of air = 15 x 1.3 = 19.5 kg
(v) By law of floatation,
Mass of the air displaced = total mass of hydrogen, balloon and equipment
Substituting the values in the formula we get,
19.5 = 8.5 + x
x = 19.5 – 8.5 = 11 kg
Hence, mass of the equipment = 11 kg