Consider a balloon of mass 0.030 kg being inflated with a gas of density 0.54 kgm-3.
What will be the volume of the balloon when it just begins to rise in air of density 1.29 kg m-3? [g = 10 ms-2]
Consider a balloon of mass 0.030 kg being inflated with a gas of density 0.54 kgm-3.
What will be the volume of the balloon when it just begins to rise in air of density 1.29 kg m-3? [g = 10 ms-2]
I saw the answer 0.04 but I don't know how they arrive at that answer
Bye
To find the volume of the balloon when it just begins to rise in air, we need to calculate the buoyant force and then use it to determine the volume.
1. Calculate the buoyant force:
The buoyant force can be calculated using the following formula:
Buoyant force = Weight of the displaced fluid
The weight of the displaced fluid can be calculated using the formula:
Weight = Mass x Gravity
In this case, the fluid is air and its density is given as 1.29 kg/m^3. The mass of the fluid displaced by the balloon is equal to the mass of the balloon itself, which is given as 0.030 kg. And the gravity is given as 10 m/s^2.
So the buoyant force can be calculated as:
Buoyant force = (0.030 kg) x (10 m/s^2)
2. Calculate the weight of the balloon:
The weight of the balloon can be calculated using the formula:
Weight = Mass x Gravity
In this case, the mass of the balloon is given as 0.030 kg and the gravity is given as 10 m/s^2.
So the weight of the balloon can be calculated as:
Weight of the balloon = (0.030 kg) x (10 m/s^2)
3. Set up the equilibrium equation:
When the balloon just begins to rise, the buoyant force is equal to the weight of the balloon. So we can set up the following equation:
Buoyant force = Weight of the balloon
4. Calculate the volume:
To calculate the volume, we can rearrange the equilibrium equation and substitute the values we calculated:
(0.030 kg) x (10 m/s^2) = (Density of air) x (Volume) x (Gravity)
Rearranging the equation to solve for the volume:
Volume = [(0.030 kg) x (10 m/s^2)] / [(Density of air) x (Gravity)]
Substituting the given values:
Volume = [(0.030 kg) x (10 m/s^2)] / [(1.29 kg/m^3) x (10 m/s^2)]
Simplifying the equation:
Volume = 0.030 kg / 1.29 kg/m^3
Calculating the volume:
Volume ≈ 0.0234 m^3
Therefore, the volume of the balloon when it just begins to rise in air of density 1.29 kg/m^3 is approximately 0.0234 m^3.