The area of cross-section of the wider tube shown in figure is $800$ $cm^2$. If a mass of $12$ $ kg $ is placed on the massless piston, the difference in heights $h$ in the level of water in the two tubes is  …….. $cm$

A fire hydrant delivers water of density $\rho $ at a volume rate $L$. The water travels vertically upward through the hydrant and then does $90^o$ turn to emerge horizontally at speed $V$. The pipe and nozzle have uniform cross-section throughout. The force exerted by the water on the corner of the hydrant is

Diagram shows a jar filled with two non mixing liquids $1$ and $2$ having densities ${\rho _1}$ and  ${\rho _2}$  respectively. A solid ball, made of a material of density  ${\rho _3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${\rho _1}$ ,  ${\rho _2}$ and ${\rho _3}$  ?

A boat having a length of $3\,metre$ and breadth $2\,metre$ is floating on a lake. The boat sinks by one cm when a man gets on it. Mass of the man is ……. $kg$

A thin vertical uniform wooden rod is pivoted at the top and immersed in water as shown. The container is slowly raised. At a certain moment, the equilibrium becomes unstable. If density of water is $9/5$ times the density of wood, then ratio of total length of rod to the submerged length of rod, at that moment is