$A$ wooden piece floats half-submerged in a tub of water. If the system is transferred to a lift ascending with acceleration $a$,the wooden piece will:

$A$ body floats with $\frac{1}{n}$ of its volume outside of water. If the body is pushed to a depth $h$ inside the water and released,it will come to the surface after time $t$. Then:

The weight of an empty balloon on a spring balance is $w_1$. The weight becomes $w_2$ when the balloon is filled with air. Let the weight of the air itself be $w$. Neglect the thickness of the balloon when it is filled with air. Also,neglect the difference in the densities of air inside and outside the balloon. Then:

$A$ body when fully immersed in a liquid of specific gravity $1.2$ weighs $44 \text{ gwt}$. The same body when fully immersed in water weighs $50 \text{ gwt}$. The mass of the body is (in $\text{ g}$)

$A$ non-conducting body floats in a liquid at $20^{\circ} C$ with $\frac{2}{3}$ of its volume immersed in the liquid. When the liquid temperature is increased to $100^{\circ} C$,$\frac{3}{4}$ of the body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of the container of the liquid):

Two non-mixing liquids of densities $\rho$ and $n\rho$ $(n > 1)$ are put in a container. The height of each liquid is $h$. $A$ solid cylinder of length $L$ and density $d$ is placed in this container. The cylinder floats with its axis vertical and a length $pL$ $(p < 1)$ submerged in the denser liquid. The density $d$ is equal to: