Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
$(A)$ $d_Ad_F$ $(B)$ $d_B > d_F$ $(C)$ $d_A>d_F$ $(D)$ $d_A+d_B=2 d_F$
$(A,B,D)$
$(A,B,C)$
$(A,C,D)$
$(B,C,D)$
A log of wood of mass $120 Kg$ floats in water. The weight that can be put on the raft to make it just sink, should be ....... $Kg$ (density of wood = $600 Kg/m^3$)
If $W$ be the weight of a body of density $\rho $ in vacuum then its apparent weight in air of density $\sigma $ 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
A liquid is kept in a closed vessel. If a glass plate (negligible mass) with a small hole is kept on top of the liquid surface, then the vapour pressure of the liquid is the vessel is