$(a)\;\large\frac{2QEt}{m_{0}+m n t}\qquad(b)\;\large\frac{QEt}{m_{0}+m n t}\qquad(c)\;\large\frac{QEt}{2(m_{0}+m n t)}\qquad(d)\;None$

Answer : (b) $\;\large\frac{QEt}{m_{0}+m n t}$

Explanation :

Two forces will act on the tank .

(a) Electrostatic force (b) Thrust force

Let v be the velocity at any instant . Then

$F_{net}=QE-mvn$

$(m_{0}+mnt)\;\large\frac{dv}{dt}=QE-mnv$

$\int_{0}^{v}\;\large\frac{dV}{QE-mnv}=\int_{0}^{t}\;\large\frac{dt}{m_{0}+mnt}$

$ln(\large\frac{QE}{QE-mnv})=ln(\large\frac{m_{0}+mnt}{m_{0}})$

$m_{0}QE=m_{0}QE-m_{0}mnv+QEmnt-m^2n^2vt$

$v=\large\frac{QEt}{m_{0}+mnt}\;.$

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