The area of cross section of the wides tube shown in the figure is $800\,cm^2$. If a mass of $12\,kg$ is placed on the massless piston, the difference in the heights $h$ in the level of water in two tubes ........ $m$
$10$
$6$
$15$
$2$
A square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4\,h$ from the surface of water in a water tank kept on a horizontal surface. If $l << h,\,r << h$ and the rate of water flow from the holes is the same, then $r$ is equal to
A spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_1 (\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous} = -kv^2 (k > 0)$. The terminal speed of the ball is
A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, $R$ is equal to
If the terminal speed of a sphere of gold (density $= 19.5\, kg/m^3$) is $0.2\, m/s$ in a viscous liquid (density $= 1.5\, kg/m^3$), find the terminal speed of a sphere of silver (density $=10.5\, kg/m^3$) of the same size in the same liquid ........ $m/s$
Two liquids having densities $d_1$ and $d_2$ are mixed in such a way that both have same mass. The density of the mixture is ............