Which of the following statements about a fluid at rest in a cup is/are correct ? 1. Pressure is same at all the points in the fluid. 2. Pressure is exerted on the walls. 3. Pressure exists everywhere in the fluid. Select the correct answer using the code given below :
- (a)1 and 2 only
- (b)2 and 3 only
- (c)1 only
- (d)1, 2 and 3
Correct — B, 2 and 3 only. Statement 3 is right: a fluid at rest presses in every direction at every point within it, not merely downwards, so there is a definite pressure at each point in the liquid. Statement 2 follows from that: because the pressure at a point acts equally in all directions, the fluid pushes sideways against the walls of the cup as well as down on its base — which is why a dam has to be built thick at the bottom and why a punctured hole in the side of a can squirts water outwards. Statement 1 fails, because the pressure at a point in a resting liquid is not one single number for the whole cup. It grows steadily with depth, by the weight of the column standing above the point, so the bottom of the cup carries more pressure than a point just under the surface.
- (a)1 and 2 only — It picks up the false statement 1 and drops the true statement 3. Pressure is not uniform through a resting fluid — it rises with depth, as the formula for the pressure due to a liquid column makes plain.
- (c)1 only — The one statement selected here is the only false one of the three. Whoever chooses this has confused the equal-in-all-directions property at a point with equality between points at different depths.
- (d)1, 2 and 3 — The trap for anyone who ticks statements off as they read. Two of the three are correct, and the sweeping option fails on statement 1 alone.
Pressure at a point in a liquid at rest is the weight of the liquid column standing above that point, spread over unit area, and it equals density × g × depth. It therefore depends on how deep the point is and on how dense the liquid is, but not on the width of the vessel or the shape of the container — which is the reason liquid stands at the same level in every arm of a many-limbed vessel. At any one point, the pressure acts equally in all directions; that property is what makes a liquid push outwards on the walls of its container and upwards on the base of a body floating in it.
The item hinges on a single distinction that catches candidates out year after year: pressure at a point is the same in every DIRECTION, but pressure is not the same at every DEPTH. Statement 1 borrows the wording of the first fact and applies it to the second, and only the words 'at all the points' give the switch away. A quick physical check helps too — if pressure really were uniform throughout, water would not spurt harder from a hole near the bottom of a bucket than from one near the top, and a diver would feel no more squeeze at thirty metres than at three. It is worth noticing that nothing in this item depends on the cup, since the pressure at a given depth is unaffected by the vessel's width or shape.
- Pressure due to a liquid column equals density × acceleration due to gravity × depth.
- At any one point in a resting fluid, pressure acts equally in all directions.
- Pressure therefore acts on the side walls of a container as well as on its base.
- Pressure increases with depth, so it is not the same at every point in the fluid.
- For a given depth and liquid, pressure does not depend on the shape or width of the vessel.
Equal in every direction at a point; unequal between points at different depths.
- Turning 'equal in all directions at a point' into 'equal at all points', which is the whole trick of statement 1.
- Thinking a wider vessel means greater pressure at the same depth; the width does not enter the formula.
- Forgetting that a resting liquid presses sideways at all, which is what makes dams thick at the base.
NDA sets fluid statics either as a multi-statement code item like this one or as a single question about what the pressure at the base of a beaker depends on.
A liquid is kept in a glass beaker. Which one of the following statements is correct regarding the pressure exerted by the liquid column at the base of the beaker?
- (a) The pressure depends on the area of the base of the beaker
- (b) The pressure depends on the height of liquid column
- (c) The pressure does not depend on the density of the liquid
- (d) The pressure neither depends on the area of the base of the beaker nor on the height of liquid column
Answer(b) The pressure depends on the height of liquid column
The keyed answer here settles statement 1 of the 2018 item. If pressure depends on the height of the column above a point, it must differ between a point near the surface and one at the base.
All objects experience a buoyancy when they are immersed in a fluid. Buoyancy is
- (a) a downward force
- (b) a downward pressure
- (c) an upward force
- (d) an upward pressure
Answer(c) an upward force
Buoyancy exists only because pressure rises with depth, so this item is the direct consequence of the fact that sinks statement 1 above.
- practice — not a real PYQ
The pressure at a point inside a liquid at rest depends on
- (a)the area of the base of the vessel
- (b)the depth of the point and the density of the liquid
- (c)the total volume of liquid in the vessel
- (d)the shape of the vessel
Answer(b) the depth of the point and the density of the liquid — pressure equals density × g × depth.
- practice — not a real PYQ
A dam is built much thicker at its base than at its top because
- (a)the base has to carry the weight of the wall above it only
- (b)water pressure increases with depth
- (c)the water is denser near the bottom
- (d)the pressure of water acts only downwards
Answer(b) water pressure increases with depth — so the sideways push on the wall is greatest at the bottom.