$A$ rectangular block of mass $M$ and cross-sectional area $A$ floats on a liquid of density $\rho$. It is given a small vertical displacement from equilibrium; it starts oscillating with frequency $n$. Then:

$A$ solid cube is floating in a liquid. The coefficient of linear expansion of the cube is $\alpha$ and the coefficient of volume expansion of the liquid is $\gamma$. On increasing the temperature of the (liquid + cube) system,the cube will sink if

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:

Assertion $(A)$: $A$ helium-filled balloon does not rise indefinitely in the air but halts after a certain height.
Reason $(R)$: Viscosity opposes the motion of the balloon. Choose any one of the following four responses:

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with an acceleration of $g/3$, the fraction of volume immersed in the liquid will be

$A$ cylindrical block of wood of base area $30 \, cm^2$ floats in a liquid of density $900 \, kg/m^3$. The block is depressed lightly and then released. The time period of the resulting oscillations of the block is equal to that of a spring with a block of the same mass. The spring constant is equal to ........ $N/m$.