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Q.

Consider a horizontally oriented syringe containing water located of a height of 1.25 m above the ground. The diameter of plunger is 8 mm and the diameter of the nozzle is 2 mm. The plunger is pushed with a constant speed of $0.25 {ms}^{- 1}$ . Find the horizontal range of water stream on the ground. Take $g = 10 {ms}^{- 2} .$

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a

4 m

b

2 m

c

10 m

d

20 m

answer is B.

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Detailed Solution

Question Image

By continuity equation between C and A

AV = av

$\begin{array}{l} \frac{π}{4} D^{2} V = \frac{π}{4} d^{2} v \\ v = {(\frac{D}{d})}^{2} V = {(\frac{8}{2})}^{2} \times 0 .25 = 4 {ms}^{- 1} \end{array}$

Projectile motion between A and B

Question Image

$\begin{array}{l} h = \frac{1}{2} {gt}^{2} \\ t = \sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 \times 1 .25}{10}} \\ = 0 .5 s \\ R = vt = 4 \times 0 .5 = 2 m \end{array}$

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