A boat floating in a tank is carrying some passengers. If the passengers drink water from the tank, how will it affect the water level of the tank?
- AIt will go down
- BIt will rise
- CIt will depend on the atmospheric pressure
- DIt will remain same
Solution & Step-by-step Explanation
Let the total mass of the boat and the passengers be , and the mass of the water drunk by the passengers be .
1. According to Archimedes' principle, a floating body displaces a volume of water whose weight is equal to the weight of the floating body.
2. Initially, the boat displaces a volume corresponding to its total mass .
3. When the passengers drink a mass of water from the tank, the total volume of water directly present in the tank decreases by an amount equal to the volume of mass .
4. However, because the mass is now inside the passengers, the total mass of the boat-passenger system becomes . As a result, the boat sinks slightly lower and displaces an additional volume of water exactly equal to the volume of mass .
Since the volume of water removed from the tank is perfectly balanced by the additional volume of water displaced by the heavier boat system, the overall water level remains the same.
1. According to Archimedes' principle, a floating body displaces a volume of water whose weight is equal to the weight of the floating body.
2. Initially, the boat displaces a volume corresponding to its total mass .
3. When the passengers drink a mass of water from the tank, the total volume of water directly present in the tank decreases by an amount equal to the volume of mass .
4. However, because the mass is now inside the passengers, the total mass of the boat-passenger system becomes . As a result, the boat sinks slightly lower and displaces an additional volume of water exactly equal to the volume of mass .
Since the volume of water removed from the tank is perfectly balanced by the additional volume of water displaced by the heavier boat system, the overall water level remains the same.