$A$ small air bubble is at the inner surface of the bottom of a beaker filled with cold water. Now,the water in the beaker is heated. The size of the bubble increases. The reason for this may be:

  • A
    Increase in the saturated vapour pressure of water
  • B
    Root mean square velocity of air molecules inside the bubble increases
  • C
    Decrease in surface tension of water
  • D
    All of the above

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$A$ liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides. If the radius of the vessel is $0.05\,m$ and the speed of rotation is $2\,rev/s$,the difference in the height of the liquid at the center of the vessel and its sides will be .............. $cm$ $(\pi^2 = 10)$.

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When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. Taking the atmospheric pressure to be equal to $10 \ m$ height of water column,the depth of the lake would approximately be ....... $m$ (ignore the surface tension and the effect of temperature).

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