A light metal stick of square cross-section $\left(5 \mathrm{cm}\times 5 \mathrm{cm}\right)$ and length$\text{'}4 \mathrm{m}\text{'}$ mass $2.5 \mathrm{kg}$ is shown in the figure below. Determine its angle (in degrees) of inclination when the water surface is $1 \mathrm{m}$ above the hinge.

A wooden plank of length $1 \mathrm{m}$ and uniform cross-section is hinged at one end to the bottom of a tank as shown in figure. The tank is filled with water upto a height $0.5 \mathrm{m}.$ The specific gravity of the plank is $0.5.$ Find the angle $\theta$ (in degrees) that the plank makes with the vertical in the equilibrium position. (exclude the $\cos \theta =0°).$

The diagram shows venturimeter through which water is flowing. The speed of water at $X$ is $2 \mathrm{cm} {\sec }^{-1}.$ Find the speed of water $\left(\mathrm{in} \mathrm{cm} {\sec }^{-1}\right)$ at $Y$  $\left(\mathrm{taking} g=1000 \mathrm{cm} {\sec }^{-2}\right).$

In a movable container shown in figure a liquid of density $\rho$ is filled up to a height $h$ $(1.8 \mathrm{m}).$ The upper $\&$ lower tube cross sectional areas are $A_2 \&{ A}_1$ respectively $\left(A_2>>A_1\right).$ If the liquid leaves out the container through the tube of cross-sectional area $A_1$ then find the velocity of liquid $\left(\mathrm{in} \mathrm{m} {\sec }^{-1}\right)$ coming out. $\left(\mathrm{Take} \mathrm{g}=10 \mathrm{m} {\sec }^{-2}\right)$

A large tank is filled with two liquids of specific gravities $2\mathrm{\sigma }$ and $\mathrm{\sigma }.$ Two holes are made on the wall of the tank as shown. Find the ratio of the distance from $O$ of the points on the ground where the jets from holes $A \text{\&} B$ strike. If the ratio is $\sqrt{\frac{a}{b}},$ find the value of $(a+b).$