Two solids $A$ and $ B$ float in water. It is observed that $A$ floats with half its volume immersed and $B$ floats with $2/3$ of its volume immersed. Compare the densities of $A$ and $B$
$4:3$
$2:3$
$3:4$
$1:3$
A solid sphere of density $\eta$ $( > 1)$ times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m then the tension in the string is given by
Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is $36 g $ and its density is $9 g / cm^3$. If the mass of the other is $48 g$, its density in $g / cm^3$ is
A ball whose density is $0.4 \times 10^3\,kg/m^3$ falls into water from a height of $9\,cm$ . To what depth does the ball sink ? ....... $cm$
A hydraulic automobile lift is designed to lift cars with a maximum mass of $3000\, kg$. The area of cross section a of piston carrying the load is $425\, cm ^{2}$. What is the maximum pressure () would smaller piston have to bear ?
A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density $0.8$ and with its vertex submerged. When another liquid of relative density $\rho$ is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is $0.10$ $m$ and the radius of the circular base is $0.05$ $m$. The specific gravity $\rho$ is given by