
Solution by using Bernoulli's principle and equation of continuity Comparing points $A$ and $B$
$A_A V_A=A_B V_B$ {equation of continuity}
$\because A_A < A_B$
$v_A > v_B$
$P_A+\frac{1}{2} \rho V_A^2+\rho g h=P_B+\frac{1}{2} \rho V_B^2+\rho g h$ {Bernoulli's equation}
$\because v_A > v_B$
$\Rightarrow \frac{1}{2} \rho V_A^2 > \frac{1}{2} \rho V_B^2$
$\therefore P_A < P_B \quad \ldots (1)$
Now comparing $C$ and $B$
$A_B=A_C \Rightarrow v_B=v_C$
[equation of continuity].
$P_B+\frac{1}{2} \rho V^2+\rho g h_B=P_C+\frac{1}{2} \rho V^2+\rho g h_C$
$\Rightarrow P_B+\rho g h_B=P_C+\rho g h_C$
$\because h_B > h_C \text { then } \quad \ldots (2)$
$P_B < P_C$
Using $(1)$ and $(2)$
We can say, $P_A < P_B < P_C$

(The coefficient of viscosity of water is $9.8 \times 10^{-6}$ $\left.\mathrm{N} \mathrm{s} / \mathrm{m}^2\right)$
[Given: $\pi=22 / 7, g=10 ms ^{-2}$, density of water $=1 \times 10^3 kg m ^{-3}$, viscosity of water $=1 \times 10^{-3} Pa$-s.]
$(A)$ The work done in pushing the ball to the depth $d$ is $0.077 J$.
$(B)$ If we neglect the viscous force in water, then the speed $v=7 m / s$.
$(C)$ If we neglect the viscous force in water, then the height $H=1.4 m$.
$(D)$ The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is $500 / 9$.