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There is a metal cube inside a block of ice which is floating on the surface of water. The ice melts completely and metal falls in the water. Water level in the
container
- a)Rises
- b)Falls
- c)Remains same
- d)Nothing can be concluded
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
There is a metal cube inside a block of ice which is floating on the s...
Vt = total volume, Vi = volume of ice, Vm = volume of metal, Vw = volume of water
Vt = Vw + Vi + Vm
Since Mi = Mw and ρi x Vi = (ρw)i x (Vw)i and ρi < (ρw)i
So, Vi > (Vw)i
Finally, Vt = (Vw)i + Vi + Vm
Vt = Vw + Vi + Vm
Since Mi = Mw and ρi x Vi = (ρw)i x (Vw)i and ρi < (ρw)i
So, Vi > (Vw)i
Finally, Vt = (Vw)i + Vi + Vm
Most Upvoted Answer
There is a metal cube inside a block of ice which is floating on the s...
Explanation:
When the ice cube melts, the metal cube falls into the water. The water displaced by the metal cube is equal to its volume. Since the metal cube is denser than water, it displaces less water than its own volume. This means that the water level in the container will decrease.
To understand this, let's consider the following points:
- Archimedes' Principle states that any object partially or completely submerged in a fluid (liquid or gas) experiences an upward force called buoyancy which is equal to the weight of the fluid displaced by the object.
- Ice is less dense than water. When a block of ice is floating on water, it displaces its own weight of water.
- The metal cube is denser than water. When it is placed in the ice, it displaces its own volume of ice (which is less than its own volume of water).
- When the ice melts, the melted water takes up the same volume as the displaced ice, but the metal cube displaces less water than its own volume.
- Therefore, the water level in the container decreases.
In summary, the water level in the container falls when the metal cube falls into the water after the ice cube melts.
When the ice cube melts, the metal cube falls into the water. The water displaced by the metal cube is equal to its volume. Since the metal cube is denser than water, it displaces less water than its own volume. This means that the water level in the container will decrease.
To understand this, let's consider the following points:
- Archimedes' Principle states that any object partially or completely submerged in a fluid (liquid or gas) experiences an upward force called buoyancy which is equal to the weight of the fluid displaced by the object.
- Ice is less dense than water. When a block of ice is floating on water, it displaces its own weight of water.
- The metal cube is denser than water. When it is placed in the ice, it displaces its own volume of ice (which is less than its own volume of water).
- When the ice melts, the melted water takes up the same volume as the displaced ice, but the metal cube displaces less water than its own volume.
- Therefore, the water level in the container decreases.
In summary, the water level in the container falls when the metal cube falls into the water after the ice cube melts.
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