An empty glass jar is submerged in tank of water with open mouth of the jar downwards, so that air inside the jar is trapped and cannot get out. As the jar is pushed down slowly, the magnitude of net buoyant force on the system of volume of gas trapped in the jar and the jar

If $W$ be the weight of a body of density $\rho $ in vacuum then its apparent weight in air of density $\sigma $ is

A concrete sphere of radius $R$  has a cavity of radius $ r$  which is packed with sawdust. The specific gravities of concrete and sawdust are respectively $2.4$  and $0.3$  for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be

A spring balance reads $200 \,gF$ when carrying a lump of lead in air. If the lead is now immersed with half of its volume in brine solution, what will be the new reading of the spring balance? specific gravity of lead and brine are $11.4$ and $1.1$ respectively ........... $gF$

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

Two solids $A$  and $ B$  float in water. It is observed that $A$  floats with $\frac{1}{2}$ of its body immersed in water and $ B$  floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of $ A$  to that of $B$  is