The weight of a body in water is one third of its weight in air. The density of the body is ....... $g / cm ^3$
$0.5$
$1.5$
$2.5$
$3.5$
A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water 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
A dumbbell is placed in water of density $\rho$ . It is observed that by attaching a mass $m$ to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass $m$ is negligible. The value of length $l$ is
A cylindrical block of area of cross-section $A$ and of material of density $\rho$ is placed in a liquid of density one-third of density of block. The block compresses a spring and compression in the spring is one-third of the length of the block. If acceleration due to gravity is $g$, the spring constant of the spring is:
A metallic body of material with density of $8000\ kg/m^3$ has a cavity inside. A spring balance shows its mass to be $10.0\ kg$ in air and $7.5\ kg$ when immersed in water. The ratio of the volume of the cavity to the volume of the material of the body must be