The tension in a massless cable connected to an iron ball of $100 \,kg$ when it is submerged in sea water is (Given: $\rho_{\text{iron}} = 8 \times 10^3 \,kg/m^3$, $\rho_{\text{sea water}} = 1000 \,kg/m^3$, $g = 10 \,m/s^2$). (in $\,N$)

$A$ 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 ............... $m$.

$A$ cube of side $40 \ cm$ is floating with $\frac{1}{4}$th of its volume immersed in water. When a circular disc is placed on the cube, it floats with $\frac{2}{5}$th of its volume immersed in water. The mass of the disc is (in $kg$)

$A$ block of steel of size $5 \times 5 \times 5 \, cm^3$ is weighed in water. If the relative density of steel is $7$,its apparent weight is ........... $g wt$.

$A$ 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

$A$ thin uniform cylindrical shell,closed at both ends,is partially filled with water. It is floating vertically in water in a half-submerged state. If $\rho_c$ is the relative density of the material of the shell with respect to water,then the correct statement is that the shell is