(Solved): Mercury is poured into a U-tube with two cylindrical arms of different radii. Both arms are cylind ...

Mercury is poured into a U-tube with two cylindrical arms of different radii. Both arms are cylindrical tubes. The left arm of the tube has a radius of \( 8.4 \mathrm{~cm} \), and the right arm has a radius of \( 3.2 \mathrm{~cm} .100 \mathrm{~g} \) of water are then poured into the right arm. Given that the density of mercury is \( 13.6 \mathrm{~g} / \mathrm{cm}^{3} \), and density of water is \( 1 \mathrm{~g} / \mathrm{cm}^{3} \) to what height \( h \) above the mercury level in the right arm, does the mercury rise in the left arm? State your answer in centimetres to the nearest hundredth of \( \mathrm{cm} \). Use \( g=9.8 \mathrm{~m} / \mathrm{s}^{2} \)