Figure $($a$)$ below shows a U$-$shaped tube containing an amount of mercury. The left arm of the tube has cross$-$sectional area

A$1$

of $10\mathrm{.}2$ cm$2,$ and the right arm has a cross$-$sectional area

A$2$

of $5\mathrm{.}30$ cm$2.$ In both arms, the mercury is at the same level, as shown.

In figure $($b$)$ below, $200$ g of water is poured into the right arm of the tube and sits atop the mercury, all of it within the right arm. The mercury level in the right arm has been displaced downward, and the mercury level in the left arm has been displaced upward from its original level by a distance h$.$ The density of mercury is $13\mathrm{.}6$ g$/$cm$3,$ and the density of water is $1\mathrm{.}00$ g$/$cm$3.$

Figure $($a$)$ shows a U$-$shaped tube filled with mercury. Both arms of the U$-$shaped tube are vertical. The left arm with cross$-$sectional area A$1$ is wider than the right arm with cross$-$sectional area A$2.$ The height of the mercury is the same in both arms. Figure $($b$)$ shows the same U$-$shaped tube, but now most of the right arm is filled with water. The height of the column of water in the right arm is much greater than the height of the column of mercury in the left arm. The height of the mercury in the left arm is greater than the height of the mercury in the arms in Figure $($a$),$ and the difference in height is labeled h$.$

$($a$)$

What is the length $($in cm$)$ of the column of water in the right arm of the U$-$shaped tube?

cm

$($b$)$

What distance h $($in cm$)$ does the mercury rise in the left arm?