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 '$$B$$' of surface tension and density double the values of liquid '$$A$$', the height of liquid column raised in liquid '$$B$$' would be (Assume angle of contact same)

A particle of mass '$$\mathrm{m}$$' is rotating along a circular path of radius '$$r$$' having angular momentum '$$L$$'. The centripetal force acting on the particle is given by

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the process is $$\left(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\gamma=\frac{3}{2}\right) \quad(\mathrm{R}=$$ gas constant $$)$$