A solid is completely immersed in a liquid. The force...

A solid is completely immersed in a liquid. The force exerted by the liquid on the solid will :
(a) increase if it pushed deeper inside the liquid
(b) change if its orientation is changed
(c) decrease if it is taken partially out of the liquid
(d) none of the above

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure in a fluid increases with depth due to the weight of the fluid above. However, when an object is completely immersed, the forces exerted on different parts of the object result in a net buoyant force that remains the same regardless of how deep the object is submerged, since the pressure differences depend only on the vertical dimensions of the object.

Orientation Independence in Fluid Statics

The buoyant force on a submerged object is independent of its orientation. This is because the net force is determined by the overall volume of displaced fluid and the density of the fluid, not by how the object is rotated or positioned in the fluid. The pressure on every point of the object's surface may change with orientation, but the integrated effect over its entire surface remains constant when fully immersed.

Archimedes' Principle

Archimedes' Principle states that any object wholly or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. This principle explains why the buoyant force depends solely on the volume of fluid displaced, and not on the depth at which the object is immersed, as long as the object is fully submerged in a fluid of uniform density.

Transcript

00:01 In this question, it is given that there is a solid body which is completely immersed in a liquid.

00:11 So when it is completely immersed in a liquid, what will be the force exerted by the fluid on the solid body? that's what we need to determine.

00:20 So the first option is given as increase the bion force, the force exerted by the liquid will increase if it is a push deeper inside the liquid.

00:32 That means the weight of the solid body will be acting in a vertically downward direction and the force exerted by the liquid that is the buoyant force fb will be acting on the solid body in an upward direction.

00:56 So this buoyant force will be equal to the weight of the volume of the water displaced.

01:04 That is, you can say that row g into volume v.

01:10 So in this relation we can find that there is no relation between the buoyant force and the depth or height.

01:19 So therefore, the given option a is not correct.

01:26 Then coming to the option b, it is given that if the orientation is changed, what will happen to the buoyant force? that is what we need to find it out.

01:39 Now, if we change the orientation of the solid body, what happens? the same weight of the body will be acting in the vertically downward direction, the bi -en force will be acting in the vertically upward direction, and the magnitude of the bi -en -force will not change at all.

01:57 The bi -enforce b will be equal to row g into v...

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