UPSC Prelims 2007 Q120: Science & Technology – Physics
- (a) Vessel B
- (b) All the vessels A, B and C will be emptied simultaneously
- (c) Vessel A
- (d) Vessel C
Answer: (b) All the vessels A, B and C will be emptied simultaneously
Explanation
Draining vessels of water, mercury and kerosene — Torricelli's law
Torricelli's law: speed of liquid leaving a hole = v = √(2gh).
It depends only on the height (h) of liquid above the tap — not on density.
| Vessel | Liquid | Density | Outflow speed at same h |
|---|---|---|---|
| A | Water | 1.0 g/cm³ | √(2gh) |
| B | Mercury | 13.6 g/cm³ | √(2gh) — same |
| C | Kerosene | ~0.8 g/cm³ | √(2gh) — same |
Mercury has more weight pressing down, but it also has more mass to push out.
The two effects cancel exactly.
So with identical vessels, taps and starting height, all three empty at the same time.
Key note: The answer key stored for this question is (d) Vessel C.
That is not supported by physics — even viscosity does not favour kerosene (kerosene is more viscous than water).
The standard physics answer, used by most answer keys, is (b).
Answer: (b) All the vessels A, B and C will be emptied simultaneously.
Why each option is right or wrong
- (a) Incorrect. Mercury's high density gives more pressure but also more mass — outflow speed is the same.
- (b) CORRECT. By Torricelli's law, outflow speed √(2gh) does not depend on density, so all three empty together.
- (c) Incorrect. Water has no special advantage — same height, same speed.
- (d) Incorrect. Low density does not speed up draining; kerosene is in fact slightly more viscous than water.
Key point
Torricelli: v = √(2gh) — independent of density. Same height + same taps → all vessels empty together.
Remember
Outflow speed from a tap depends on liquid height, not density — so all three empty together.
Common mistakes
- Thinking the heavier liquid (mercury) pushes out faster — its extra mass cancels the extra pressure.
- Thinking the lighter liquid (kerosene) flows out faster — density does not appear in Torricelli's formula.
- Bringing in viscosity wrongly — it is not what the question tests, and it would not favour kerosene anyway.
Exam tip
Like Galileo's falling bodies: in a free-fall-type problem, mass/density cancels. Torricelli's v = √(2gh) is just free-fall speed.
Sources
- NCERT Class XI — Physics Part II, Ch 10 (Mechanical Properties of Fluids — Torricelli's law)
- UPSC_KEY_DISPUTES.md — Q2069