Question

an engine of power 9.8 kW is used to pump water from a mine 40m deep calculate the mass of water it can pump out in 1 hour ...formula and explanations please. .​

Answer 1

ANSWER

Power (P) =4.9kilowatt

=4.9×1000watt

=4900watts

Depth of a well (h) = 50 meter

Acceleration due to gravity

g=9.8ms  

−2

 

t=1hour

=60×60=3600s

P=  

time

workdone

​  

=  

t

mgh

​  

 

4900=  

3600

m×9.8×50

​  

 

3600×4900=m×9.8×50

m=  

9.8×50

3600×4900

​  

=36000kg

∴ Volume of water pumped per hour

=36000litre

=36.0litre         (∴ 1 litre = 1 kg)

=36kilolitre

Answer 2

The mass of mine is 6.94Kg.

Given:

An engine of power 9.8 kW is used to pump water from a mine 40m deep and calculate the mass of water it can pump out in 1 hour.

To Find:

The mass of mine is 6.94Kg.

Solution:

To find the mass of mine is 6.94Kg. we will follow the following steps:

As we know,

Power = Work done × time

Power = m×g×h × time

Here, m is the mass of water

g is the acceleration due to gravity = 9.8ms-².

h is the height of mine = 40m

time = 1 hour = 60 ×60 = 3600seconds

As we have to calculate mass. so,

$mass = \frac{power}{g \times h \times time} = \frac{9.8 \times 1000}{9.8 \times 3600 \times 40}$

Now,

Putting values in the above formula we get,

$mass = \frac{1}{144} gram$

$= \frac{1}{144} \times 1000 = 6.94kg$

Henceforth, the mass of mine is 6.94Kg.

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