Water rises upto a height of $$4 \mathrm{~cm}$$ in a capillary tube. The lower end of the capillary tube is at a depth of $$8 \mathrm{~cm}$$ below the water level. The mouth pressure required to blow an air bubble at the lower end of the capillary will be '$$\mathrm{X}$$' $$\mathrm{cm}$$ of water, where $$\mathrm{X}$$ is equal to

The initial pressure and volume of a gas is '$$\mathrm{P}$$' and '$$\mathrm{V}$$' respectively. First by isothermal process gas is expanded to volume '$$9 \mathrm{~V}$$' and then by adiabatic process its volume is compressed to '$$\mathrm{V}$$' then its final pressure is (Ratio of specific heat at constant pressure to constant volume $$=\frac{3}{2}$$)

A particle is performing U.C.M. along the circumference of a circle of diameter $$50 \mathrm{~cm}$$ with frequency $$2 \mathrm{~Hz}$$. The acceleration of the particle in $$\mathrm{m} / \mathrm{s}^2$$ is

The frequency of a tuning fork is $$220 \mathrm{~Hz}$$ and the velocity of sound in air is $$330 \mathrm{~m} / \mathrm{s}$$. When the tuning fork completes 80 vibrations, the distance travelled by the