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 $11\mathrm{.}0c{m}^2,$ and the right arm has a cross$-$sectional area $A_2$ of $6\mathrm{.}00c{m}^2.$ In both arms, the mercury is at the same level, as shown.

In figure $($b$)$ below, $400$ 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 $13\mathrm{.}6\frac{g}{c}{m}^3,$ and the density of water is $1\mathrm{.}00\frac{g}{c}{m}^3.$

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

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

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