How High Does Mercury Rise in a U-Tube When Water is Added?

[Phyeng]

Homework Statement

A long U-tube contains mercury (density = 14 × 103 kg/m3). When 2.0 cm of water (density = 1.0 × 103 kg/m 3) is poured into the left arm, the mercury in the right arm rises above its original level by

Homework Equations

Density*gravity*height(on the left arm)=density*gravity*height(on the right arm)

The Attempt at a Solution

Using the above equation I got the answer 0.143cm(rounded) but that isn't the final answer.because 0.143 cm is the height difference between two sides of the mercury.
I think the answer is 0.071cm because if 0.14cm of fluid moved to the right arm and to put this tube back into equilibrium, half of that fluid that has to move from right side to the other side? therefore if half of 0.143 moved to the other side, then the distance moved from original poistion would be 0.143-(0.143/2)=0.071.
I am not sure if this is right, But if it sounds right to anyone, please say so, so i can be sure that I'm right. Thanks you very much for spending time to read, Very much appreciated.

 

[1994Bhaskar]

NO YOU ARE WRONG.THE EQUATIONS APPLIED BY YOU GIVE DIRECTLY THE FINAL STATE IN EQUILIBRIUM.THE FINAL ANSWER 0.143=DISTANCE TRAVELED BY MERCURY IN LEFT ARM (DOWNWARDS)+DISTANCE TRAVELED BY MERCURY IN RIGHT ARM(UPWARDS).
AS THE QUESTION IS "mercury in the right arm rises above its original level by" THUS ANSWER IS 0.0714