A sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

If the terminal speed of a sphere of gold (density $19.5 \,kg / m ^2$ ) 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 is ............ $m / s$

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 homogeneous solid cylinder of length $L(L < H/2)$, cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure $P_0$. Then, density $D$ of solid is given by

Equal mass of three liquids are kept in there identical cylindrical vessels $A, B $ $\&$ $ C$. The densities are $\rho_A$, $\rho_B$ and $\rho_C$ with $\rho_A < \rho_B < \rho_C$ . The force on base will be maximum in vessel:-

What is the pressure on a swimmer $20 \,m$ below the surface of water is ..... $atm$