The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $$5 \mathrm{~cm}$$. If the tube is dipped in a similar manner in another liquid $$\mathrm{B}$$ of surface tension and density double the values of liquid $$\mathrm{A}$$, the height of liquid column raised in liquid $$\mathrm{B}$$ would be __________ m.

Choose the correct relationship between Poisson ratio $$(\sigma)$$, bulk modulus (K) and modulus of rigidity $$(\eta)$$ of a given solid object :

A fully loaded boeing aircraft has a mass of $$5.4\times10^5$$ kg. Its total wing area is 500 m$$^2$$. It is in level flight with a speed of 1080 km/h. If the density of air $$\rho$$ is 1.2 kg m$$^{-3}$$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($$\mathrm{g=10~m/s^2}$$)

Surface tension of a soap bubble is $$2.0 \times 10^{-2} \mathrm{Nm}^{-1}$$. Work done to increase the radius of soap bubble from $$3.5 \mathrm{~cm}$$ to $$7 \mathrm{~cm}$$ will be:

Take $$\left[\pi=\frac{22}{7}\right]$$