$A$ very large block of ice of the size of a volleyball court and of uniform thickness of $8 \,m$ is floating on water. $A$ person standing near its edge wishes to fetch a bucketful of water using a rope. The smallest length of rope required for this is about ............... $m$.

$A$ block of volume $V$ and density $\sigma_b$ is placed in a liquid of density $\sigma_l$ (where $\sigma_l > \sigma_b$). If the block is moved upward by a height $h$ while remaining completely submerged in the liquid,what is the increase in the gravitational potential energy of the system?

$A$ wooden cylinder floats vertically in water with half of its length immersed. The density of wood is

$A$ pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. $A$ container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it is balanced. $A$ brass weight on the end of a string is then lowered into the water,but not allowed to rest on the bottom of the container. What happens next?

$A$ block of wood of volume $V$ floats in water with half of its volume submerged. The same block floats in an oil with $0.8 \,V$ volume submerged. If the density of water is $1000 \,kg \,m^{-3}$, then the density of the oil is

$A$ piece of steel has a weight $W$ in air,$W_1$ when completely immersed in water,and $W_2$ when completely immersed in an unknown liquid. The relative density (specific gravity) of the liquid is: