$A$ cube of wood supporting a $200 \, g$ mass just floats in water. When the mass is removed,the cube rises by $2 \, cm$. The side of the cube is ............ $cm$.

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:

To determine the composition of a bimetallic alloy,a sample is first weighed in air and then in water. These weights are found to be $w_1$ and $w_2$ respectively. If the densities of the two constituent metals are $\rho_1$ and $\rho_2$ respectively,then the weight of the first metal in the sample is (where $\rho_w$ is the density of water):

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

$A$ boat carrying a number of stones is floating in a water tank. If the stones are unloaded into the water,the water level in the tank will ............

$A$ candle of diameter $d$ is floating on a liquid in a cylindrical container of diameter $D$ $(D >> d)$ as shown in the figure. If it is burning at the rate of $2 \text{ cm/hour}$,then the top of the candle will: