Question

A balloon of volume $100m{s^{ - 1}}$ is filled with hot air of density $0.40 kgm{s^{ - 1}}.$ If the fabric of balloon weighs $16kgf$ and equipment P is attached to it, such that balloon is in the state of equilibrium. Calculate weight of combined hot air and balloon?
$
A.{\text{ 46kgf}} \\
B.{\text{ 40kgf}} \\
{\text{C}}{\text{. 56kgf}} \\
{\text{D}}{\text{. 50kgf}} \\
$

Answer 1

Hint:The unit of force is given in kgf (kilogram-force) is the non standard gravitational metric unit. First convert the kgf in Newton units. First convert all the given units in the same format and then use the standard formulas to calculate weight and mass and then find the combined weight.

Complete step by step answer:
Given that the fabric of the balloon weight is $16kgf$. Convert the Kgf in Newton.
$1kgf = 10N$
Therefore, the weight of the fabric balloon is $ = 16\;{\text{Kgf}}$ ${\text{ = 16}} \times {\text{10N}}$
The weight of the balloon fabric is ${\text{ = 160N}}$
Hence, the mass of the balloon fabric is $m = 16kg$ ...... (a)
Now, from the given values of volume and density find the values for the Mass of hot air.
$Mass,M = volume \times density$
Place the given values in the above equation
$M = 100 \times 0.4 \\
\Rightarrow M = 40kg \\ $
Mass of hot air is $M = 40kg$ ...... (b)
Total weight of the equipment is –
$W = (m + M)g$
By using the values of equations (a) and (b), place the values in the above equations and g is the acceleration gravity, where $g = 10m/{s^2}$ and simplify –
$W = (40 + 16) \times 10 \\
\Rightarrow W = 560N \\ $
As the required answer is in Kgf unit, convert Newton in Kgf.
$W = \dfrac{{560}}{{10}}Kgf$
$ \therefore W = 56Kgf$
Therefore, the combined weight of hot air and balloon is $56Kgf$

Hence, from the given multiple choices – the option C is the correct answer.

Note: Always double check the given units, make sure to have all the given units in the same format before substituting in the formulas. Also, remember the basic conversion relations among the physical quantities and apply accordingly.