Two cubes of size $1.0 \ m$ sides,one of relative density $0.60$ and another of relative density $1.15$ are connected by a weightless wire and placed in a large tank of water. Under equilibrium,the lighter cube will project above the water surface to a height of ........ $cm$.

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):

$A$ boat having a length of $3\,m$ and breadth $2\,m$ is floating on a lake. The boat sinks by $1\,cm$ when a man gets on it. The mass of the man is ....... $kg$. (Take density of water $\rho = 1000\,kg/m^3$ and $g = 10\,m/s^2$)

$A$ glass flask weighing $390 \ g$,having an internal volume of $500 \ cm^3$,just floats when half of it is filled with water. The specific gravity of the glass is:

Two solids $P$ and $Q$ float in water. It is observed that $P$ floats with half of its volume immersed and $Q$ floats with $\frac{2}{3}$ of its volume immersed. The ratio of densities of $P$ and $Q$ is

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$,the fraction of volume immersed in the liquid will be: