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What is the power of an engine which can lift $20 metric tons$ of coal $per hour$ from a $20 - metre$ deep mine?

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1.09 \times 1 0^{3} Watt

2.09 \times 1 0^{3} Watt

3.09 \times 1 0^{3} Watt

4.09 \times 1 0^{3} Watt

answer is A.

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Detailed Solution

Power of an engine which can lift

20 metric tons

of coal

per hour

from a

20 meter

deep mine is given by

1.09 \times 1 0^{3} Watt

.
Given
Mass

m = 20 metric ton = 20 \times 1000 kg,

Distance

s = 20 m

,
Time

t = 1 hour = 3600 s

The capacity to do work is termed Energy. The Energy expended to do work in unit time is
termed Power. It is represented as P.
Power Formula is articulated as,

P = \frac{E}{t}

P = \frac{W}{t}

Where
The Energy Consumed to do work

= E

Work done

= W

Time taken

= t

Power =

\frac{work}{time}

Power =

\frac{mg \times s}{t}

Power =

\frac{20 \times 1000 \times 9.8 \times 20}{3600}

Power =

1.09 \times 1 0^{3} Watt

Hence Power of an engine is

1.09 \times 1 0^{3} Watt

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What is the power of an engine which can lift 20 metric tons of coal per hour from a 20-metre deep mine?

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What is the power of an engine which can lift $20 metric tons$ of coal $per hour$ from a $20 - metre$ deep mine?