A cylindrical container of radius $R=50 \mathrm{~cm}$ is filled with water up to a height $h_{o} .$ Upon rotating the cylinder about its central axis at a constant angular speed, the free surface takes a parabolic shape (see figure), and is displaced upwards by $h_{1}=10 \mathrm{~cm}$ at $r=R$. The magnitude of the downward displacement $h_{2}$ of the free surface at $r=0$ is_______________ $\mathrm{cm}$ (round off to the nearest integer).

A cylindrical container of radius $R=50 \mathrm{~cm}$ is filled with water up to a height $h_{o} .$ Upon rotating the cylinder about its central axis at a constant angular speed, the free surface takes a parabolic shape (see figure), and is displaced upwards by $h_{1}=10 \mathrm{~cm}$ at $r=R$. The magnitude of the downward displacement $h_{2}$ of the free surface at $r=0$ is_______________ $\mathrm{cm}$ (round off to the nearest integer).

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