Problem $3(10$ points$)$:

The gate shown here has a mass of $180$ kg $,$ is $1\mathrm{.}2$ meter wide $($in the plane of the page$).$ The hinge is at the top

$($Point $A)$ and it is resting on a smooth surface on the bottom $($Point $B).$ Let the density of water be: $p=998k\frac{g}{m^3}.$

Let the length of the gate, $l,$ be $1$ meter and the angle, $$ be $60.$ Assuming there is zero force acting at Point $B,$

what must the density of the kerosene be$?$

Solution:

Solve problem and show work on paper please.