A hollow spherical shell at outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ $w.r.t.$ water, the value of $r$ is$......R$

A hollow sphere of mass $M$ and radius $r$ is immersed in a tank of water (density $\rho$$_w$ ). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle $45^o$ with the horizontal as shown in the figure. The tension $T_1$ in the wire is :

A solid sphere of density $\eta$ $( > 1)$  times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m then the tension in the string is given by

A cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. ....... $kg$ is the maximum weight that can be put on the block without fully submerging it under water ? [Take density of water $= 10^3\,kg/m^3$ ]

A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water

There are two identical small holes of area of cross-section a on the opposite sides of a  tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. Tank  is resting on a smooth horizontal surface. Horizontal force which will have to be  applied on the tank to keep it in equilibrium is