Find the apparent weight of a metallic block of density $5 \text{ g cm}^{-3}$ and dimensions $5 \text{ cm} \times 5 \text{ cm} \times 5 \text{ cm}$,in water.

$A$ $0.5\ kg$ mass of lead is submerged in a container filled to the brim with water and a block of wood floats on top. The lead mass is slowly lifted from the container by a thin wire and as it emerges into air the level of the water in the container drops a bit. The lead mass is now placed on the block of wood. As the lead is placed on the wood,what happens to the water level in the container?

Two cubical blocks identical in dimensions float in water in such a way that the $1$st block floats with half part immersed in water and the $2$nd block floats with $3/4$ of its volume inside the water. The ratio of densities of the blocks is ..........

When does a body sink in a liquid? Explain.

An object with uniform density $\rho$ is attached to a spring that is known to stretch linearly with applied force. When the spring-object system is immersed in a liquid of density $\rho_1$,the spring stretches by an amount $x_1$ (where $\rho > \rho_1$). When the experiment is repeated in a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$),the spring stretches by an amount $x_2$. Neglecting any buoyant force on the spring,the density of the object is:

$A$ silver ingot weighing $2.1 \ kg$ is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of silver is $10.5$. The tension in the string in $kg-wt$ is