Water flows at the rate of 2ms^-1 through a pipe of radius 2 cm and emerges from a nozzle of radius 1 cm. If the nozzle is directed vertically upwards, water rises to a maximum height of $\left(\mathrm{g}=10 {\mathrm{ms}}^{-2}\right)$

Given,

${\mathrm{V}}_1=2\mathrm{m}/\mathrm{s}, {\mathrm{r}}_1=2\mathrm{cm}=2\times {10}^{-2}\mathrm{m}$

${\mathrm{A}}_1={{\mathrm{\pi r}}_1}^2=\mathrm{\pi }\times 4\times {10}^{-4}{\mathrm{m}}^2$

for nozzle let ,

$\mathrm{velocity}={\mathrm{V}}_2$

${\mathrm{r}}_2=1\mathrm{cm}=1\times {10}^{-2}\mathrm{m}$

${\mathrm{A}}_2=\mathrm{\pi }\times {\left({10}^{-2}\right)}^2 =\mathrm{\pi }\times {10}^{-4}$

By equation of continuity,

${\mathrm{A}}_1{\mathrm{V}}_1={\mathrm{A}}_2{\mathrm{V}}_2$

$4\mathrm{\pi }\times {10}^{-4}\times 2=\mathrm{\pi }\times {10}^{-4}\times {\mathrm{V}}_2$

${\mathrm{V}}_2=8\mathrm{m}/\mathrm{s}$

${\mathrm{v}}^2={\mathrm{u}}^2-2\mathrm{gh}$

$0=8^2-2\times 10\times \mathrm{h}\Rightarrow 20\mathrm{h}=64\Rightarrow \mathrm{h}=\frac{64}{20}=3.2\mathrm{m}$

Hence the correct answer is 3.2 m.