$A$ certain block weighs $15 \ N$ in air. It weighs $12 \ N$ when immersed in water. When immersed in another liquid,it weighs $13 \ N$. The relative density of the block is:

$A$ body floats in water with $40 \%$ of its volume outside water. When the same body floats in an oil, $60 \%$ of its volume remains outside oil. The relative density of oil is

$A$ wooden cube first floats inside water when a $200\,g$ mass is placed on it. When the mass is removed,the cube rises $2\,cm$ above the water level. The side of the cube is ........ $cm$.

$A$ wooden block with a coin placed on its top floats in water as shown in the figure. $l$ and $h$ are as shown. After some time,the coin falls into the water. Then:

Two bodies having volumes $V$ and $2V$ are suspended from the two arms of a common balance and they are found to balance each other. If the larger body is immersed in oil (density $d_1 = 0.9 \ gm/cm^3$) and the smaller body is immersed in an unknown liquid,the balance remains in equilibrium. The density of the unknown liquid is given by ......... $gm/cm^3$.

$A$ 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