An incompressible box is completely submerged in MERCURY at a depth of 13 yd. The MERCURY density is the same at all depths. As the box gets deeper, which of the following will REMAIN CONSTANT? Choose all that apply.
volume of mercury displaced
weight of displaced mercury
box mass
depth of the box
box weight
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Also, Google Archimedes and
weight = mass * acceleration of gravity
To determine which quantities will remain constant as the incompressible box gets deeper in the mercury, we can analyze each option one by one:
1. Volume of mercury displaced: The volume of liquid displaced by a submerged object is equal to the volume of the object itself. Since the box is incompressible, its volume will remain constant regardless of the depth. Therefore, the volume of mercury displaced by the box will also remain constant. Hence, this option is correct.
2. Weight of displaced mercury: The weight of a liquid displaced by an object is equal to the weight of the object itself. Since the density of mercury is the same at all depths, the weight of the mercury displaced by the box will remain constant. Therefore, this option is also correct.
3. Box mass: The mass of the box does not depend on the depth at which it is submerged. Therefore, regardless of the depth, the box mass will remain constant. Hence, this option is correct.
4. Depth of the box: This option is incorrect. As the box gets deeper in the mercury, the depth of the box will increase.
5. Box weight: The weight of an object is equal to its mass multiplied by the acceleration due to gravity (w = m * g). Since the box mass remains constant and the acceleration due to gravity does not change, the weight of the box will also remain constant. Therefore, this option is correct.
In summary, the options that will remain constant as the incompressible box gets deeper in the mercury are:
- Volume of mercury displaced
- Weight of displaced mercury
- Box mass
- Box weight