Volume of the plastic balloon = 15 m^{3}

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**