Two copper vessels A and B have the same base area but of different sh...
In hydrostatic condition,
P = P0 + ρgh
Here, P : absolute pressure at depth h, P0 is atmospheric pressure
Since, height of liquid in both vessel is same therefore pressure on the base of both vessel will be same.
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Two copper vessels A and B have the same base area but of different sh...
Explanation:
To understand the given scenario, let's consider the following points:
1. Same Base Area:
Both vessels A and B have the same base area. This means that the area of contact between the vessels and the surface on which they are placed is the same.
2. Different Shapes:
The vessels have different shapes, so their heights and volumes will differ even if they have the same base area.
3. A takes twice the volume of water as B:
This means that the volume of water required to fill vessel A up to a particular height is twice the volume required to fill vessel B up to the same height.
4. Pressure on the base area:
The pressure exerted on the base area of a vessel depends on the weight of the liquid above it and the area of contact between the vessel and the surface. The pressure at the same height in both vessels will be the same because the base areas are the same.
Now, let's consider the options:
a) Vessel B weighs twice that of A:
This statement cannot be concluded because the weight of a liquid depends on its volume and density. Since the density of the liquid is not given and the volumes are different, we cannot determine the weight of the liquid in each vessel.
b) Pressure on the base area of vessels A and B is the same:
This statement is correct. As explained earlier, the pressure exerted on the base area of a vessel depends on the weight of the liquid and the area of contact. Since the base areas are the same and the height of the liquid is the same, the weight of the liquid above the base area will be the same in both vessels, resulting in the same pressure.
c) Pressure on the base area of vessels A and B is not the same:
This statement is incorrect. As explained earlier, the pressure on the base area is the same in both vessels.
d) Both vessels A and B weigh the same:
This statement cannot be concluded because the weight of a liquid depends on its volume and density, which are not given.
Therefore, the correct statement among the options is b) Pressure on the base area of vessels A and B is the same.
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