Question

An engine pumps water continuously to a hose of area of cross section 2 x 10-'m-2. The water comes out with a velocity of 2ms ? What is the
power supplied to water
(A) 2W
(B) 4W
(C) 6W
(D) 16 W​

Answer 1

Answer:

Option D 16 W is the answer

Answer 2

Given:

An engine pumps water continuously to a hose of area of cross section 2 x 10^(-3) m-2. The water comes out with a velocity of 2m/s. Density of water = 1000 kg/m³.

To find:

Power delivered to water.

Calculation:

Power can be represented as the product of force and velocity.

$\therefore \: \sf{P = force \times velocity}$

$= > \: \sf{P = f \times v}$

$= > \: \sf{P = (mass \times acceleration) \times v}$

$= > \: \sf{P = (m \times a) \times v}$

$= > \: \sf{P = (m \times \dfrac{v}{t} ) \times v}$

$= > \: \sf{P = ( \rho \times volume )\times \dfrac{ {v}^{2} }{t} }$

$= > \: \sf{P = ( \rho \times area \times length)\times \dfrac{ {v}^{2} }{t} }$

$= > \: \sf{P = ( \rho \times a \times l)\times \dfrac{ {v}^{2} }{t} }$

$= > \: \sf{P = \{\rho \times a \times (v \times t) \}\times \dfrac{ {v}^{2} }{t} }$

$= > \: \sf{P = \rho \times a \times {v}^{3} }$

$= > \: \sf{P = 1000 \times 2 \times {10}^{ - 3} \times {(2)}^{3} }$

$= > \: \sf{P = 2 \times 8 }$

$= > \: \sf{P = 16 \: watt }$

So, final answer is:

$\boxed{ \: \bf{Power = 16 \: watt }}$