An air bubble of volume $50\, cm^3$ is formed at the bottom of a lake $47.6\, m$ deep. What will be its volume when it reaches the surface? (Atmospheric pressure $= 70\, cm$ of $Hg$ and density of $Hg = 13.6\, g/cm^3$)

State whether the following statements are True or False:
$(i)$ The Bernoulli equation can be considered to be a statement of the conservation of energy.
$(ii)$ The angle of contact between a drop of water and the material of a raincoat is an acute angle.
$(iii)$ The absence of roughness between two consecutive layers of fluid is the definition of viscosity.

$A$ cylindrical vessel partially filled with water is rotated about its vertical central axis. Its surface will

$A$ razor-blade floats on the surface of water contained in a glass. When the glass is gently shaken,the razor-blade sinks. Mark the incorrect statement.

Two vessels of equal cross-sectional area $A$ are filled with a liquid of density $d$. The height of the liquid in one vessel is $h_1$ and in the other vessel is $h_2$. When both vessels are connected,find the work done by gravity.

$Assertion :$ $A$ thin stainless steel needle can float on a still water surface.
$Reason :$ Any object floats when the buoyancy force balances the weight of the object.