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Water flows at the rate of $4 m / s$ through a pipe of radius $4 c m$ and emerges from a nozzle of radius $2 c m$ . If the nozzle is directed vertically upwards. Water rises to a maximum height of $(g = 10 m / s^{2})$

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$6.4 m$

$9.2 m$

$5.8 m$

$12.8 m$

answer is D.

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Detailed Solution

$π r_{1}^{2} v_{1} = π r_{2}^{2} v_{2}$

$\Rightarrow r_{1}^{2} v_{1} = r_{2}^{2} v_{2} \Rightarrow r_{1}^{2} v_{1} = r_{2}^{2} \sqrt{2 g h}$

${(4)}^{2} \times 4 = 2^{2} \times \sqrt{2 g h}$

$\Rightarrow 16 \times 4 = 4 \times \sqrt{2 g h}$

$256 = 2 g h$

$\Rightarrow h = \frac{256}{20} = \frac{128}{10} = 12.8 m$

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