Question

in a hydro electric power , 1000×10power3kg water falls through a height of 51m in one second. calculate (1) work done by the following water and (2) power generated under ideal conditions ​

Answer 1

Answer:

Given:

Mass of water = 1000 × 10³ kg

Height through which it falls = 51 metres

Time taken = 1 second

To find:

• Work done by water
• Power generated under ideal conditions

Concept:

For calculation of work done , we can easily understand that the whole Potential energy of the water at that height will be converted to work done while falling.

This is because gravitational force is an conservative force.

And finally power can be calculated as the rate of work done .

Calculation:

$\boxed{potential \: energy = m \times g \times h}$

$= > PE = {10}^{6} \times 10 \times 51$

$= > PE = 51 \times {10}^{7} joules$

This whole PE will be converted to work done by water.

$\boxed{ \red{ \therefore \: work = 51 \times {10}^{7} \: joules }}$

Now , Calculation of power :

$power = \dfrac{work}{time}$

$= > power = \dfrac{51 \times {10}^{7} }{1}$

$= > power = 51 \times {10}^{7} watts$

$\boxed{ \red { power = 510000 \: kilowatts}}$

Answer 2

$\Huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Given :

• Mass (m) = 1000 × 10³ kg
• Height (h) = 51 m
• Time (t) = 1 s

Solution :

As, we know that. Work Done = Potential Energy by Work Energy Theorem

So,

$\large \bigstar {\boxed{\sf{Work \: = \: mgh}}} \\ \\ \\ \implies {\sf{Work \: = \: 1000 \: \times \: 10^3 \: \times \: 10 \: \times \: 51}} \\ \\ \\ \implies {\sf{Work \: = \: 1000 \: \times \: 10^4 \: \times \: 51}} \\ \\ \\ \implies {\sf{Work \: = \: 51 \: \times \: 10^7}} \\ \\ \\ \large {\boxed{\sf{Work \: Done \: is \: 51 \: \times \: 10^7 \: J}}}$

$\rule{200}{2}$

And formula for Power is :

$\large \bigstar {\boxed{\sf{Power \: = \: \dfrac{Work}{Time}}}} \\ \\ \\ \implies {\sf{Power \: = \: \dfrac{51 \: \times \: 10^7}{1}}} \\ \\ \\ \implies {\sf{Power \: = \: 51 \: \times \: 10^7}} \\ \\ \\ \large {\boxed{\sf{Power \: is \: 51 \: \times \: 10^7 \: W}}}$

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Additional Information :

Power :

• Power is defined as rate of Work done.
• Power = Work Done /Time
• Power is measures in Watt (W)
• Power is Scaler Quantity

Work Done :

• It is defined as When a force is applied to change distance of object is Work done.
• Work Done = F*s
• Measured in Joules (J)
• It is a scaler quantity