A spherical solid ball of volume $V$ is made of a material of density ${\rho _1}$ . It is falling through a liquid of density ${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$. Assume that the liquid applies a viscous force on the ball that is propoertional to the square of its speed $v$ , i.e., ${F_{{\rm{viscous}}}} = - k{v^2}\left( {k > 0} \right)$. Then terminal speed of the bal is
$\sqrt {\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}} $
$\frac{{Vg{\rho _1}}}{k}$
$\sqrt {\frac{{Vg{\rho _1}}}{k}} $
$\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}$
An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2\, m/s$. The mass per unit length of water in the pipe is $100\, kg/m$. ......... $W$ is the power of the engine .
A candle of diameter $d$ is floating on a liquid in a cylindrical container of diameter $D\left( {D > > d} \right)$ as shown in figure. If it is burning at the rate of $2\ cm/hour$ then the top of the candle will
A space $2.5\ cm$ wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area $0.5\ m^2$ just midway the surfaces at a speed of $0.5\ m/sec$ is $1\ N$. The coefficient of viscosity in $kg-s/m^2$ is
If work done in increasing the size of a soap film from $10\, cm\times6\, cm$ to $60\, cm\times11\, cm$ is $2\times10^{-4}\, J$. What is the surface tension ?
A hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho $ . sphere is moving horizontally with an acceleration $2\ g$ , where $g$ is acceleration due to gravity in the space. If minimum pressure of liquid is $P_0$ , then pressure at the centre of sphere is