An ice block contains a glass ball when the ice melts within the water containing vessel, the level of water

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

A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3 p$. The complete arrangement is placed in a liquid of density $2 p$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are)

$(A)$ the net elongation of the spring is $\frac{4 \pi R^3 \rho g}{3 k}$

$(B)$ the net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$

$(C)$ the light sphere is partially submerged.

$(D)$ the light sphere is completely submerged.

An object is fitted in a hole at base of a container as shown in figure, the force due to liquid on object is (Assume no leakage of water, volume of object inside container is $V$ and density of liquid is $\rho $ )

Why does a ship made of iron float while a piece of iron sinks in water ?