$A$ 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 = $1000 \ kg/m^3$).

$A$ body is suspended by a light string. The tensions in the string when the body is in air,when the body is totally immersed in water,and when the body is totally immersed in a liquid are respectively $40.2 \,N$,$28.4 \,N$,and $16.6 \,N$. The density of the liquid is

An object weighs $m_1$ in a liquid of density $d_1$ and $m_2$ in a liquid of density $d_2$. The density $d$ of the object is

$A$ body floats in a liquid contained in a beaker. The whole system falls freely under gravity. The upthrust on the body due to the liquid is

Two solid pieces,one of steel and the other of aluminium,when immersed completely in water,have equal weights. When the solid pieces are weighed in air:

$A$ hollow spherical shell of outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ with respect to water,the value of $r$ is $......R$.