Please refer to the image attached.
The Attempt at a Solution
Since ρ and g are constant, therefore h1:h2 must be 2:1.
But the answer is 18:12. Why am I wrong?
... And only one of the offered answers is consistent with p > 0. That is all you are asked to do. There is not enough information to deduce the exact ratio.Not when you take the ratio of the two heights. The ratio h1/h2 is 2:1 only if p=0.
The ratio is h1 : h2 = 16000-p : 8000-p. p > 0. You cannot determine the ratio exactly, but only one of the offered ratios is consistent with these facts. That is why the question is worded this way. It does not ask you which of the offered answers is the ratio, it asks which could be the ratio.and if P=/=0, then I can only solve the simultaneous equations by subtraction?
You are right, you can calculate the difference and that does answer the question. But it is still the case that there is not enough information to determine the two heights - it is merely a matter of saying which pair of heights is feasible, and that can be resolved by either method.Actually it does not say or ask anything about a ratio. All discussion about ratio was just a wrong start. There is not point to insist along that path.
They give you the density of the mercury so you can calculate the actual value of the difference. (6 cm).