$A$ cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. What is the maximum weight (in $kg$) that can be put on the block without fully submerging it under water? [Take density of water $= 10^3\,kg/m^3$]

$A$ stone of relative density $K$ is released from rest on the surface of a lake. If viscous effects are ignored, the stone sinks in water with an acceleration of

An object suspended by a wire stretches it by $10 \,mm$. When the object is immersed in a liquid,the elongation in the wire reduces by $\frac{10}{3} \,mm$. The ratio of the relative densities of the object and the liquid is ............

State the law of floatation and describe its cases.

$A$ 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

$A$ cylindrical block floats vertically in a liquid of density $\rho_{1}$ kept in a container such that the fraction of volume of the cylinder inside the liquid is $x_{1}$. Then some amount of another immiscible liquid of density $\rho_{2} (\rho_{2} < \rho_{1})$ is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with $x_{2}$ being the fraction of volume of the cylinder inside the liquid of density $\rho_{1}$. The ratio $\rho_{1} / \rho_{2}$ will be