Question

The mass of equipment using the law of floatation is x kilogram (kg). Find x−5.
A. 11
B. 5
C. 7
D. 6

Answer 1

Hint: To solve this question we use the basic theory related to the Principle of Floatation. As we know, the law of floatation states that any object placed in a liquid experiences an upward force which allows the body to float in water. floatation depends upon the density Mainly.

Complete answer:
We calculated the mass of a body by the formula, Mass=Density × Volume.
The volume of the balloon is the volume of hydrogen that will be present in the balloon, that is, 15${{\text{m}}^{\text{3}}}$ The density of hydrogen is 0.09kg/${{\text{m}}^{\text{3}}}$
Therefore, In the balloon, the mass of hydrogen = 15 $\times$ 0.09 = 1.35kg.
7.15 kg is given as the mass of the balloon.
So, total mass of hydrogen + mass of the balloon = 1.35+7.15=8.50kg
Let us have the mass of the equipment be taken as y.
Therefore,
We calculate the total mass of the floating body by 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, 15${{\text{m}}^{\text{3}}}$.
The density of air is 1.3kg/${{\text{m}}^{\text{3}}}$
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 = 6 kg.

So, the correct answer is “Option D”.

Note:
When a body floats with its volume partially above the liquid surface, the volume of the liquid displaced by the body is equal to the volume of the submerged portion of the body. Since the body is in equilibrium, the force of buoyancy acting on the body must be equal to its weight.