Question

The mass of equipment using the law of floatation is $Xkg$. Find $X-5$.

• A. $11$
• B. $5$
• C. $7$
• D. $6$

Answer 1

Answer: (D)

$6$

The mass of a body is calculated from the formula, $Mass=Density\times Volume$.
The volume of the balloon is the volume of hydrogen that will be present in the balloon, that is, $15m^3$. The density of hydrogen is $0.09kg/m^3$.
Therefore, the mass of hydrogen in the balloon = $15\times 0.09=1.35kg.$ The mass of the balloon is given as 7.15 kg.
So, mass of hydrogen + mass of the balloon = $1.35+7.15=8.50kg$
Let us have the mass of the equipment as $y$.
Therefore, the total mass of the floating body = mass of hydrogen + balloon + equipment =$8.5+y$ ....................(1)

The volume of the balloon is the volume of hydrogen that will be present in the balloon. So the volume of air that would be displaced will also be the same, that is, $15m^3$. The density of air is $1.3kg/m^3$.
Therefore, the mass of the air displaced =$15\times 1.3=19.5kg$.................(2)
According to the laws of flotation, the total mass of the floating body is equal to the total mass of the air displaced.
Equating (1) and (2), we get $8.5+y=19.5$
$y=19.5-8.5=11kg$.
Hence, the total mass of the equipment is $11kg=x$.
Now, $x-5=6kg$.
Hence the answer is 6 kg.