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}} $
$\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}$
What is the pressure on a swimmer $20 \,m$ below the surface of water is ..... $atm$
The work done in splitting a drop of water of $1\, mm$ radius into $10^6$ droplets is (surface tension of water $72\times10^{-3}\, N/m$) :
A solid cylinder of mass $m$ and volume $v$ is suspended from ceiling by a spring of spring constant $k$ . It has cross-section area $A$ . It is submerged in a liquid of density $\rho $ upto half its length. If a small block of mass $M_o$ is kept at the centre of the top, the amplitude of small oscillation will be
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 large open tank has two holes in its wall. One is a square of side $a$ at a depth $x$ from the top and the other is a circular hole of radius $r$ at depth $4 x$ 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 ..........