A pump lifts $500$ $l i t r e s$ of water from a well of depth $50$ $m e t e r$ in $98$ $s e c o n d s$ . The power of the pump is (Given $g = 9.8 m / s^{2}$ and density of water $= 1000 k g / m^{3}$ ):

9.8

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10

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5

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2.5

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Solution

The correct option is D $2.5$ kW
Mass of water lifted, $m = V ρ$
where $V$ is Volume of water and $ρ$ is density of water
$V = 500 l = 0.5 m^{3}$ and $ρ = 1000 k g / m^{3}$
$m = 0.5 \times 1000 = 500 k g$
$h = 50 m$

Work done in moving water to a height $50 m$ is $W = m g h$
$W = 500 \times 9.8 \times 50 J$

$P = \frac{W}{t} = \frac{500 \times 50 \times 9.8}{98} = 2500 W$ $= 2.5 k W$

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A pump lifts 500 litres of water from a well of depth 50 meter in 98 seconds. The power of the pump is (Given g=9.8m/s2 and density of water =1000kg/m3):

The correct option is D 2.5 kWMass of water lifted, m=Vρ where V is Volume of water and ρ is density of waterV=500l=0.5m3 and ρ=1000kg/m3m=0.5×1000=500 kgh=50 mWork done in moving water to a height 50m is W=mghW=500×9.8×50 JP=Wt=500×50×9.898=2500 W=2.5 kW

A pump lifts $500$ $l i t r e s$ of water from a well of depth $50$ $m e t e r$ in $98$ $s e c o n d s$ . The power of the pump is (Given $g = 9.8 m / s^{2}$ and density of water $= 1000 k g / m^{3}$ ):