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
$\left( {\frac{{\eta - 1}}{\eta }} \right)\,mg$
$\eta mg$
$\frac{{mg}}{{\eta - 1}}$
$(\eta - 1)\,mg$
An ice berg of density $900 Kg/m^3$ is floating in water of density $1000 Kg/m^3$. The percentage of volume of ice-cube outside the water is ...... $\%$
The spring balance $A$ reads $2\, kg$ with a block m suspended from it. $A $ balance $B$ reads $5 \,kg $ when a beaker filled with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid as shown in figure. In this situation
A slender homogeneous rod of length $2L$ floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is $0.75$. The length of rod that extends out of water is :
Water is pumped from a depth of $10 $ $m$ and delivered through a pipe of cross section $10^{-2}$ $m^2$. If it is needed to deliver a volume of $10^{-1} $ $m^3$ per second the power required will be ........ $kW$
A solid sphere of specific gravity $27$ has a concentric spherical cavity and it just sinks in water. The ratio of cavity radius to that of outer radius of sphere is