A weather forecasting plastic balloon of volune 15m³ contains hydrogen density 0.09 kg/m³. The volume of an equipment carried by the balloons is negligible compared to its own volume. The mass of the empty balloon is 7.15 kg . The balloon is floating in air of density 1.3 kg/m³. Calculate:-
i) the mass of hydrogen in balloon
ii) the mass of hydrogen and balloon
iii) the total mass of hydrogen, balloon and equipment if the mass of equipment is 'x' kg
iv) the mass of air displaced by balloon
v) the mass of equipment using law of floatation.
Answers
Given:
A weather forecasting plastic balloon of volune 15m³ contains hydrogen density 0.09 kg/m³. The volume of an equipment carried by the balloons is negligible compared to its own volume. The mass of the empty balloon is 7.15 kg . The balloon is floating in air of density 1.3 kg/m³.
To Find:
i) The mass of hydrogen in balloon
ii) The mass of hydrogen and balloon
iii) The total mass of hydrogen, balloon and equipment if the mass of equipment is 'x' kg
iv) The mass of air displaced by balloon
v) The mass of equipment using law of floatation.
Solution:
Volume of plastic balloon = 15m³
Mass of empty balloon = 7.15 kg
Density of hydrogen = 0.09 kg/m³
Density of air = 1.3 kg/m³
i) The mass of hydrogen in balloon =
Volume of balloon × Density of hydrogen
Now,
Mass of hydrogen in balloon = (15 × 0.09)kg = 1.3
ii) The mass of hydrogen and balloon =
Mass of empty balloon + Mass of hydrogen in the balloon = (7.15 + 1.35)kg = 8.5
iii) The total mass of hydrogen, balloon and equipment if the mass of equipment is 'x' kg
Given mass of equipment = x
Total mass of hydrogen, balloon and equipment = (8.5 + x) kg
iv) The mass of air displaced by balloon
Weight of air displaced by the balloon = upthrust = Volume of balloon × density of air
= 15 × 1.3 = 19.5kg
v) The mass of equipment using law of floatation.
Using law of floatation,
Mass of air displaced = Total mass of hydrogen, balloon and equipment
or, 19.5 = 8.5 + x
or, x = 11kg
Thus, mass of the equipment 11 kg.
Mass of hydrogen =P×V=.15×0.09
=1.35 kg
Total mass = mass of H+Balloon
=1.35+7.15
=8.50 kg
Mass of hydrogen =Balloon+floating
equipment=1.35+7.15+8.50 m
Mass of displaced =15×1.3=19.5 kg
So 8.5+x=19.5
x=11 kg.