$A$ horizontal fire hose with a nozzle of cross-sectional area $\frac{5}{\sqrt{21}} \times 10^{-3} \text{ m}^2$ delivers a cubic metre of water in $10 \text{ s}$. What will be the maximum possible increase in the temperature of water while it hits a rigid wall (neglecting the effect of gravity) (in $^{\circ} \text{C}$)?

Which of the following is not an illustration of viscosity?

Two cylindrical vessels of equal cross-sectional area of $2 \ m^2$ contain water up to heights of $10 \ m$ and $6 \ m$,respectively. If the vessels are connected at their bottom,then the work done by the force of gravity is (Density of water is $10^3 \ kg/m^3$ and $g = 10 \ m/s^2$):

Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if:
$(A)$ $d_A < d_F$
$(B)$ $d_B > d_F$
$(C)$ $d_A + d_B = 2d_F$
$(D)$ $d_A > d_F$

An air bubble of volume $1\,cm^3$ rises from the bottom of a lake $40\,m$ deep to the surface at a temperature of $12^{\circ}C$. The atmospheric pressure is $1 \times 10^5\,Pa$,the density of water is $1000\,kg/m^3$,and $g = 10\,m/s^2$. There is no difference in the temperature of water at the depth of $40\,m$ and on the surface. The volume of the air bubble when it reaches the surface will be $..........\,cm^3$. (in $,cm^3$)

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.