$A$ metallic sphere weighing $3 \,kg$ in air is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of the metal is $10$. The tension in the string is ........ $N$.

The weight of a sphere in air is $50 \ g$. Its weight is $40 \ g$ in a liquid at temperature $20^{\circ} C$. When the temperature increases to $70^{\circ} C$,its weight becomes $45 \ g$. The ratio of the densities of the liquid at the two given temperatures is: (in $: 1$)

When does a body float on the surface of a liquid?

Write the equation for the volume of the partially submerged part of a body floating on the surface of a liquid.

$A$ metal ball of density $7800 \ kg/m^3$ is suspected to have a large number of cavities. It weighs $9.8 \ kg$ when weighed in air and $1.5 \ kg$ less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately ....... $\%$

$A$ log of wood of mass $120 \ kg$ floats in water. The mass that can be put on the raft to make it just sink should be ....... $kg$ (density of wood = $600 \ kg/m^3$,density of water = $1000 \ kg/m^3$).