$A$ metal cube is embedded inside a block of ice that is floating on the surface of water. The ice melts completely, and the metal cube sinks into the water. What happens to the water level in the container?

$A$ box when hung from a spring balance shows a reading of $50 \,kg$. If the same box is hung from the same spring balance inside an evacuated chamber,the reading on the scale will be

$A$ boat having a length of $3\,m$ and breadth $2\,m$ is floating on a lake. The boat sinks by $1\,cm$ when a man gets on it. The mass of the man is ....... $kg$. (Take density of water $\rho = 1000\,kg/m^3$ and $g = 10\,m/s^2$)

$A$ leak-proof cylinder of length $1 \; m,$ made of a metal which has a very low coefficient of expansion,is floating vertically in water at $0^{\circ} C$ such that its height above the water surface is $20 \; cm.$ When the temperature of water is increased to $4^{\circ} C,$ the height of the cylinder above the water surface becomes $21 \; cm.$ The density of water at $T=4^{\circ} C,$ relative to the density at $T=0^{\circ} C,$ is close to

$A$ uniform rod of density $\rho$ is placed in a wide tank containing a liquid of density $\rho_0$ $(\rho_0 > \rho)$. The depth of the liquid in the tank is half the length of the rod. The rod is in equilibrium,with its lower end resting on the bottom of the tank. In this position,the rod makes an angle $\theta$ with the horizontal.

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