# Water is flowing continuously from a tap having an internal diameter 8 × 10-3 m . The water velocity as it leaves the tap is 0.4 m s-1 . The diameter of the water stream at a distance 2 × 10-1 m below the tap is close to Option 1) 5.0 × 10-3 m Option 2) 7.5 × 10-3 m Option 3) 9.6 × 10-3 m Option 4) 3.6 × 10-3 m

As we learnt in

Equation of Continuity -

Mass of the liquid entering per second at A = mass of the liquid leaving per second at B.

a1 v1 = a2 v2

- wherein

a1  and abe the area of cross section.

$\Delta =8\times 10^{-3}m$     &      $V=0.4\ ms^{-1}$

$V=\sqrt{u^{2}+2gh}=\sqrt{(0.4)^{2}+2\times 10\times 0.2}=2\ ms^{-1}$

$A_{1}V_{1}=A_{2}V_{2}=\pi \left(\frac{8\times 10^{-3}}{4} \right )\times 0.4=\pi\times \frac{d^{2}}{4}\times 2$

$\therefore\ \; d\equiv 3.6\times 10^{-3} m$

Corrrect option is 4.

Option 1)

5.0 × 10-3 m

This is an incorrect option.

Option 2)

7.5 × 10-3 m

This is an incorrect option.

Option 3)

9.6 × 10-3 m

This is an incorrect option.

Option 4)

3.6 × 10-3 m

This is the correct option.

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