The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. $A$ graph showing the speed $v$ with which the liquid is crossing points at a distance $X$ from $O$ along a radius $XO$ would look like:

$A$ pump is used to deliver water at a certain rate through a pipe. To obtain $n$ times the water in the same time,by what factor should the velocity of water,the force of water,and the power of the pump be increased?

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.

$A$ vertical cylindrical container of base area $A$ and an upper cross-section area $A_1$ making an angle $30^{\circ}$ with the horizontal is placed in an open rainy field as shown,near another cylindrical container having the same base area $A$. The ratio of the rates of collection of water in the two containers will be:

The vertical limbs of a $U$ shaped tube are filled with a liquid of density $\rho$ up to a height $h$ on each side. The horizontal portion of the $U$ tube having length $2h$ contains a liquid of density $2\rho$. The $U$ tube is moved horizontally with an acceleration $g/2$ parallel to the horizontal arm. The difference in heights in liquid levels in the two vertical limbs,at steady state,will be:

$A$ liquid flows through a horizontal tube. The velocities of the liquid in the two sections,which have areas of cross-section $A_1$ and $A_2$,are $v_1$ and $v_2$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$.