A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density $0.8$ and with its vertex submerged. When another liquid of relative density $\rho$ is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is $0.10$ $m$ and the radius of the circular base is $0.05$ $m$. The specific gravity $\rho$ is given by

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

Why is it easier to swim in sea water than in river water ?

Two cubes of size $1.0$ $m$ sides, one of relative density $0.60$ and another of relative density $=$ $1.15$ are connected by 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 ........ $cm$

A cubical block of wood $10 \,cm$ on a side floats at the interface between oil and water with its lower surface horizontal and $4\, cm$ below the interface. The density of oil is $0.6gc{m^{ - 3}}$. The mass of block is ...... $gm$

A balloon of mass $m$ contains water of mass $M$ . If it is completely immersed in water, find the apparent mass of the balloon with water in it