$A$ cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. What is the maximum weight (in $kg$) that can be put on the block without fully submerging it under water? [Take density of water $= 10^3\,kg/m^3$]

$A$ body of density $1.2 \times 10^{3} \text{ kg/m}^3$ is dropped from rest from a height $1 \text{ m}$ into a liquid of density $2.4 \times 10^{3} \text{ kg/m}^3$. Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on the surface is: (in $\text{ m}$)

$A$ body of density $d_1$ is counterpoised by $M$ of weights of density $d_2$ in air of density $d$. Then the true mass of the body is

$A$ 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

$A$ 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 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: