A $0.5\ kg$ mass of lead is submerged in a container filled to the brim with water and a block of wood floats on top. The lead mass is slowly lifted from the container by a thin wire and as it emerges into air the level of the water in the container drops a bit. The lead mass is now placed on the block of wood. As the lead is placed on the wood.

A drinking straw is dipped in a pan of water to depth d from the surface (see figure below). Now water is sucked into it up to an initial height $h_0$ and then left to oscillate. As a result, its height $y$ from the surface of the water varies periodically. Ignoring damping, the equation for $y$ is ( $g$ is the acceleration due to gravity):

A machine is blowing spherical soap bubbles of different radii filled with helium gas.It is found that, if the bubbles have a radius smaller than $1\,cm$, then they sink to the floor in still air. Larger bubbles float in the air. Assume that the thickness of the soap film in all bubbles is uniform and equal. Assume that the density of soap solution is same as that of water $\left(=1000 \,kg m ^{-3}\right)$. The density of helium inside the bubbles and air are $0.18 \,kg m ^{-3}$ and $1.23 \,kg m ^{-3}$, respectively. Then, the thickness of the soap film of the bubbles is ………. $\mu m$ (Note $1 \,\mu m =10^{-6} \,m$ )

The spring balance $A$ reads $2$ $kg$ with a block $m $ suspended from it. $A$ balance $B$ reads $5$ $kg$ when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure in this situation:

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 spring with block of same mass, then spring constant is equal to …….. $N/m$