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Q.

A house directs a horizontal jet of water moving with a velocity of 20 m/s on to a vertical wall. The cross-sectional area of the jet is 5 x 10^-4 m². If the density of water is 1000 kg / m³, the force on the wall assuming that the water comes to rest after striking the wall, is

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a

200 N

b

100 N

c

75 N

d

50 N

answer is A.

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Detailed Solution

See fig.

Question Image

Force exerted on the wall, $F = \frac{mv - mu}{t}$

Here u = 0, $∴ F = \frac{mv}{t}$

The mass of water coming out from the jet per second is

$\frac{m}{l} = \frac{volume \times density}{1} = \frac{(AV) \times d}{1}$

where A= area of cross section of the tube

and d = density of water.

$\begin{aligned} ∴ F & = {Adv}^{2} \\ = (5 \times 10^{- 4}) \times (1000) \times (20)^{2} \\ = 200 N . \end{aligned}$

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