Two water pipes $P$ and $Q$ having diameter $2\times {10}^{-2} \mathrm{m}$ and $4\times {10}^{-2} \mathrm{m}$ respectively are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is

If the terminal speed of a sphere of Gold (density$=19.5 \mathrm{kg} {\mathrm{m}}^{-3}$) is $0.2 \mathrm{m} {\mathrm{s}}^{-1}$ in a viscous liquid (density$=1.5 \mathrm{kg} {\mathrm{m}}^{-3}$), find the terminal speed of a sphere of Silver (density$=10.5 \mathrm{kg} {\mathrm{m}}^{-3}$) of the same size in the same liquid.

Water rises to a height of, $10 \mathrm{cm}$ in a capillary tube and mercury falls to a depth of, $3.42 \mathrm{cm}$ in the same capillary tube. If the density of mercury, $13.6 \mathrm{kg} {\mathrm{m}}^{-3}$ is and the angle of contact is $135°$, the ratio of surface tension for water and mercury is (angle of contact for water and glass is $0°$).