Question

Hello brainlians !!
$​\rm Numerical$
$1.)\rm A \: container \: contains\:5000\:g\:water\:at \:the\:height \:of\:60 \:m\:above\:ground. Then\:calculate \:the \:potential \:energy$
$\rm \: 2.)A \: electric \: oven \: power \: 10 \: KW \: is \: used \: for \: 3 \: hours . Find \: the \: energy \: supplied \: by \: the \: heater.$
$\rm3.)A \: motor \: is \: used \: to \: lift \: 5 \: litres \: of \: water \: from \: a \: well \: 100 \: m \: deep \: in \: 30 \: seconds \: ( g = 10 \: m/s^{2} ). Find \: the \: power \: of \: the \: motor .$
Best of luck my brainlians !


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Answer 1

Answer:

1]

Given :-

Mass = 5000 g

Height = 60 m

Acceleration due to gravity = 9.8 m/s²

To Find :-

Potential energy

Solution :-

We know that

1000 g = 1 kg

5000 g = 5000/1000 = 5 kg

PE = mgh

PE = (5)(9.8)(60)

PE = 300 × 9.8

PE = 300 × 98/10

PE = 30 × 98

PE = 2940 J

2]

Given :-

Power = 10 kW

Time = 3 hours

To Find :-

Energy'

Solution :-

E = PT

E = energy

P = Power

T = Time

E = 10 × 1000 × 3 × 60 × 60

E = 10,000 × 10800

E = 108,000,000 J

E =  1.08 × 10⁸ J

3]

Given :-

Mass = 5 kg

Height = 100 m

Time = 30 seconds

G = 10 m/s²

To Find :-

Power

Solution :-

We know that

Power = Potential Energy/Time

Power = 5 × 100 × 10/30

Power = 5 × 10 × 10/3

Power = 500/3

Power = 166.66 W

Answer 2

1) Question

A container contains 5000g water at the height of 60m above ground. Then calculate the potential energy.

Answer :-

The potential energy of the container is 2940J.

Step-by-step explanation:

To Find :-

• The potential energy.

★ Solution

Given that,

• Mass of the container = 5000g
• Height of the container = 60m

Converting, 5000g to kg,

⇒ 5000g

⇒ 5000/1000

⇒ 5kg.

We know,

Potential energy = mgh,

Where,

• m = Mass
• g = acceleration due to gravity and it's value is 9.8 m s -²
• h = Height

Therefore,

⇒ mgh

⇒ m × g × h

⇒ 5kg × 9.8 m s-² × 60m

⇒ 2940J

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2) Question

A electric oven power 10 KW is used for 3 hours find the energy supplied by the heater.

Answer :-

The energy supplied by the heater is 1.08 × 10⁸J.

Step-by-step explanation:

To Find :-

• The energy supplied by the heater.

★ Solution

Given that,

• Power of the oven = 10 kW
• The electric oven is used for [Time] = 3 hours

Converting, 10 kW to W and 3 hours to seconds,

→ 10 kW → W

⇒ 10 × 1000

⇒ 10000W

→ 3 hours → secs

⇒ 3 × 60 × 60

⇒ 10800 secs

We know,

E = P × t,

Where,

• E = Energy
• P = Power
• t = Time.

Therefore,

⇒ P × t

⇒ 10000 × 10800

⇒ 108000000 or 1.08 × 10⁸ J

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3) Question

A motor is used to lift 5 litres of water from a well 100m deep in 30 seconds (g = 10 m/s²). Find the power of the motor.

Answer :-

The power of the motor is 166.66W.

Step-by-step explanation:

To Find :-

• The power of the motor.

★ Solution

Given that,

• m = 5 litres
• g = 10 m/s-²
• h = 100m

So, Workdone by the motor is :-

Workdone = P.E. [mgh]

⇒ mgh

⇒ 5*10*100

⇒ 5000J = Work done.

Now, power :-

We know,

P = W/t

Where,

• P = Power
• W = Workdone
• t = Time

Therefore,

⇒ W/t

⇒ 5000/30

⇒ 500/3

⇒ 166.66W

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