U-Shaped Manometer, Filled with a Liquid of Unknown Density, Is $10.0 \mathrm{kPa}$

U-shaped manometer, filled with a liquid of unknown density, is connected on one side to a vessel containing gas at gauge pressure $10.0 \mathrm{kPa}$ , and the other side is open to the atmosphere (pressure 101.3 $\mathrm{kPa}$ ) . The level of the liquid in the side connected to the gas vessel is lower than on the open side. The difference in height between the two sides is $10 \mathrm{~cm}$ . What is the density of the liquid in the manometer?

A) $1.03 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$
B) $1.13 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$
C) $2.27 \times 10^{5} \mathrm{~kg} / \mathrm{m}^{3}$
D) $1.13 \times 10^{5} \mathrm{~kg} / \mathrm{m}^{3}$
E) $1.02 \times 10^{4} \mathrm{~kg} / \mathrm{m}^{3}$