If the terminal speed of a sphere A [density $$\rho_{\mathrm{A}}=7.5 \mathrm{~kg} \mathrm{~m}^{-3}$$ ] is $$0.4 \mathrm{~ms}^{-1}$$, in a viscous liquid [density $$\rho_{\mathrm{L}}=1.5 \mathrm{~kg} \mathrm{~m}^{-3}$$ ], the terminal speed of sphere B [density $$\rho_B=3 \mathrm{~kg} \mathrm{~m}^{-3}$$ ] of the same size in the same liquid is

A needle is $$7 \mathrm{~cm}$$ long. Assuming that the needle is not wetted by water, what is the weight of the needle, so that it floats on water?

$$\left[\mathrm{T}=\right.$$ surface tension of water $$\left.=70 \frac{\mathrm{dyne}}{\mathrm{cm}}\right]$$

[acceleration due to gravity $$=980 \mathrm{~cm} \mathrm{~s}^{-2}$$]

Under isothermal conditions, two soap bubbles of radii '$$r_1$$' and '$$r_2$$' combine to form a single soap bubble of radius '$$R$$'. The surface tension of soap solution is ( $$P=$$ outside pressure)

In a capillary tube having area of cross-section A, water rises to a height 'h'. If cross-sectional area is reduced to $$\frac{A}{9}$$, the rise of water in the capillary tube is