Consider the mass of liquid in the straw. The entire liquid is moving with velocity $\dot{ y }$. Applying Newtons law on it.

$F_{\text {thrust }}=u_{\text {rel }} \frac{d m}{d t}=-\rho A \dot{y}^2$

$F_{\text {pressure }}=(\rho g d) A$

$F_{\text {gravity }}=-\rho A(y+d) g$

$F_{\text {net }}=m a$

$\Rightarrow \rho A(y+d) \ddot{y}=-\rho A \dot{y}^2+\rho g d A-\rho A g(y+d)$

$\Rightarrow(y+d) \ddot{y}^2+\dot{y}^2+g y=0$

Ans. is $D$

(Note : we can't apply Bernoulli's theorem because it is not in steady state. Energy is dissipated.)