## Chapter 5 Power Synopsis

Power is the rate of work done with respect to time, i.e., power is the work done in unit time. Power is a scalar quantity.

If W amount of work is done by a body in time t, then the power, P = \(\frac{W}{t}\).

Dimensional formula of power is ML^{2}T^{-3}

In CGS system and SI, the absolute units of power are erg/s and watt (W or J/s), respectively.

1 horse power is given by, 1hp = 550 ft • lb • s^{-1} = 746 W

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## Chapter 5 Power Short And Long Answer Type Questions

**Question 1. Define power. What is the relationship between power and work done?**

**Answer:**

**Power:-**

Power is defined as the rate of doing work with respect to time.

If the amount of work W is done in time t, then power, P = \(\frac{W}{t}\).

**Question 2. What is the dimensional formula of power? What are the dimensions of power?**

**Answer:**

**Dimensional Formula Of Power:-**

= \(\frac{\text { dimension expression of work }}{\text { dimension expression of time }}=\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{~T}}\)

= ML^{2}T^{-3}

Dimensions of power are 1 in length, 2 in mass, and -3 in time.

**Question 3. What is the relationship between power and velocity?**

**Answer:**

**Relationship Between Power And Velocity:-**

We know, power = \(\frac{\text { work }(W)}{{time}(t)}\)

Suppose a small displacement s of a body takes place in the direction of a constant force F while being acted on the body for a time t.

∴ work done, W = Fs

So, power, P = \(\frac{W}{t}=\frac{F s}{t}\) = Fv, where v is the instantaneous velocity and time interval t is very small.

**Question 4. Define absolute units of power in CGS system and SI.**

**Answer:**

**Absolute Units Of Power In CGS System And SI:-**

Absolute unit of power in CGS system is erg/s.

**1erg/s:** 1 erg/s is the power of doing lerg of work in 1 second.

Absolute unit of power in SI is J/s or watt.

**1 watt:** 1 watt is the power of doing 1 joule of work in 1 second.

**Question 5. Suppose a man walks a distance of 3 m in a horizontal path in 5 s with a bucket of water in hand. Then he climbs up 3 m in a staircase in 5 s with the same bucket. Explain in which case, the man has more power.**

**Answer:**

While walking in a horizontal plane with a bucket in hand, the force of graving acts in a direction opposite to the weight of the bucket. But the displacement of the bucket is horizontal, i.e., in a direction perpendicular to the force applied on the bucket.

Hence, this is a no-work force. As the amount of work is zero, the value of power is also zero. But while going up the staircase with the bucket, work is done against gravity. As a result, value of power is not zero. Hence, power is more in the second case.

**Question 6. What do you mean by kilowatt and horsepower?**

**Answer:**

**Kilowatt And Horsepower:-**

**Kilowatt:** 1 kW (kilowatt) is defined as the power of doing 1000 J of work in Is. So, lkW = 1000W.

Horsepower: 1 horsepower is defined as the power of doing 550ft. ib of work by any machine or by a system in 1s.

∴ 1 horsepower = 550 ft • lb • s^{-1} = 746 W

**Question 7. The power of an engine is 5 horsepower. What do you mean by the above statement?**

**Answer:**

As 1 hp = 746 W, 5 hp = 5 x 746 = 3730 W.

That is, the power of the engine is 3730 W. This means that the engine can do a work of 3730 J per second.

**Question 8. Sand is falling from the lower portion of a sand-filled moving truck. How does the kinetic energy of this truck change if the power spent by the engine remains unchanged?**

**Answer:**

Power of the engine of the moving truck

= \(\frac{\text { work done by the engine }(W)}{\text { time of work done }(t)}\)

= \(\frac{\text { force } \times \text { displacement }}{\text { time }}\)

= \(\frac{\text { weight of the truck } \times \text { displacement }}{\text { time }}\)

= \(\text { weight of the truck } \times \text { average velocity }\)

= mg x v

In this case, due to the fall of sand from the truck, its mass (m) decreases gradually. But according to the question, in order to keep the power spent by the engine constant, the velocity (v) of the truck has to be increased in the same proportion.

Thus, the value of the quantity mg x v remains constant.

∴ mg x v = constant

or, mv = constant [g = constant]

Again, kinetic energy of the truck

= 1/2 mv^{2} = 1/2(mv) x v

Since v increases in spite of mv remaining constant, hence the kinetic energy of the truck increases in this case.

## Chapter 5 Power Very Short Answer Type Questions Choose The Correct Answer

Question 1. The product of applied force on a body with its speed gives a measure of its

- Power
- Energy
- Work
- Momentum

Answer: 1. Power

Question 2. Horsepower is the unit of which of the following physical quantities?

- Work
- Power
- Kinetic energy
- Potential energy

Answer: 2. Power

Question 3. Amount of work done by a machine of 1000W power in 1 minute is

- 60000 J
- 1000 J
- 600 J
- 100 J

Answer: 1. 60000 J

Question 4. A body is lifted from the ground slowly to a certain height in the first case. Again in the second case, the same body is lifted more rapidly to the same height from the ground. Which of the following statements is true?

- Though the amount of work done is same in both the cases, amount of power is higher in the first case
- Though the amount of work done is same in both the cases, amount of power is higher in the second case
- In both the cases, work and power are different
- In both the cases, work and power are same

Answer: 2. Though the amount of work done is same in both the cases, amount of power is higher in the second case

Question 5. 100W is written on an electric bulb. W is the unit for which quantity?

- Electrical energy
- Electrical power
- Electrical work
- Mechanical energy

Answer: 2. Electrical power

Question 6. Dimensional formula of power is

- MLT
^{-3} - ML
^{2}T^{3} - ML
^{2}T^{-2} - ML
^{2}T^{-3}

Answer: 4. ML^{2}T^{-3}

Question 7. Relationship between work (W) and power (P) is

- P = Wt
- P = W/t
- P = \(\frac{W}{t^2}\)
- P = \(\sqrt{W t}\)

Answer: 2. P = W/t

Question 8. The power of a pump is 490 W. How much time is required to raise 400 L of water to a height of 15 m using this pump?

- 60s
- 90s
- 120s
- 30s

Answer: 3. 120s

Question 9. Unit of power in CGS system is

- J/s
- erg/s
- W
- erg.s

Answer: 2. erg/s

Question 10. Power of the engine of a motorbike is generally expressed in which unit?

- Horsepower
- Watt
- Joule/second
- erg/second

Answer: 1. Horsepower

Question 11. Which of the following physical quantities has joule/hour as its unit?

- Work
- Kinetic energy
- Force
- Power

Answer: 4. Power

Question 12. A boy of mass 40 kg climbs up 40 steps of a staircase in 20 s. Each step is 20 cm high. What is the power applied by the boy? (g = 9.8 m/s^{2})

- 156.7 erg/s
- 156.8 J/s
- 165.84 W
- 165.84 erg/s

Answer: 2. 156.8 J/s

Question 13. Rate of doing work by a body with respect to time is called

- Force
- Power
- Energy
- Linear momentum

Answer: 2. Power

Question 14. If Y = \(\frac{\text { work }}{\text { power }}\), then the dimensional formula of Y is

- M
^{0}L^{0}T^{0} - M
^{0}L^{2}T^{0} - M
^{0}L^{2}T^{1} - T

Answer: 4. T

Question 15. Compared to one kilowatt (kW), one horsepower (hp) is

- More
- Less
- Same
- Cannot be said

Answer: 2. Less

Question 16. The relationship between horsepower and watt is

- 1hp = 476 W
- 1hp = 764 W
- lhp = 746 W
- lhp = 674 W

Answer: 3. lhp = 746 W

Question 17. If Z = \(\frac{\text { work }}{\text { power }}\) work , then which quantity is represented by Z?

- Kinetic energy
- Potential energy
- Time
- Linear momentum

Answer: 3. Time

Question 18. A train moves against a frictional force of 5000 N at a velocity of 25 m/s. What is the power of the engine of the train?

- 1250 W
- 125000 J/s
- 1.25 X 106W
- 12.5W

Answer: 2. 125000 J/s

Question 19. A boy does a work of 400 erg in 5 s and a girl takes 10 s to do the same work. Which of the following statements is correct?

- The boy has more power
- The girl has more power
- Both have the same power
- None of the above

Answer: 1. The boy has more power

Question 20. Which of the following physical quantity have the unit J/h?

- Work
- Kinetic energy
- Force
- Power

Answer: 4. Power

Question 21. Work done = power x

- Velocity
- Speed
- Time
- Displacement

Answer: 3. Time

Question 22. Which one of the following is not the unit of power?

- erg/s
- W
- W.h
- J/s

Answer: 3. W.h

## Chapter 5 Power Answer In Brief

**Question 1. What is the unit of power in SI?**

**Answer:** Watt is the unit of power in SI.

**Question 2. What is the relationship between work and power?**

**Answer:** Relationship between work and power is expressed by power = \(\frac{work}{time}\)

**Question 3. What is the relationship between power and velocity?**

**Answer:** The relationship between power and velocity is expressed by power = applied force x velocity of the body

[In this case, velocity of the body means instantaneous velocity.]

**Question 4. Horsepower is the unit of which quantity?**

**Answer:** Horsepower is the practical unit of power in FPS system.

**Question 5. 1 horsepower = how many W?**

**Answer:** 1 horsepower = 746 W.

**Question 6. 1 kW = how much horsepower?**

**Answer:** 1 kW = 1.34 horsepower

**Question 7. What do you mean by 1 kilowatt of power?**

**Answer:** One kW (kilowatt) is defined as the power required to do a work of 1000J in one second, i.e., 1 kW = 1000W.

**Question 8. The power of a pump is 1.2 kW. What do you mean by the above statement?**

**Answer:** The power of a pump is 1.2 kW means that the pump can do a work of 1.2 kJ or 1200 J in one second.

**Question 9. What is average power?**

**Answer:** Average power of is defined as the ratio of total work done to the total time taken.

i.e., average power = \(\frac{\text { total work done }}{\text { total time }}\)

## Chapter 5 Power Fill In The Blanks

Question 1. Division of the unit of work by the unit of power gives the unit of _______

Answer: Time

Question 2. Multiplication of the unit of force by the unit of ________ gives the unit of power.

Answer: Velocity

Question 3. Power x _________ = work.

Answer: Time

Question 4. Power is a ______ physical quantity.

Answer: Scalar

Question 5. Power of a motor is 373 W. In hp unit the power of the motor is ________

Answer: 0.5

Question 6. Power of an agency depends upon how fast ______ is done by it.

Answer: Work

## Chapter 5 Power State Whether True Or False

Question 1. Power is a scalar quantity.

Answer: True

Question 2. Power is the capacity of a body to do work.

Answer: False

Question 3. 1 horsepower = 746 kW.

Answer: False

Question 4. Rate of work done is power.

Answer: True

Question 5. Horsepower is a practical unit of power.

Answer: True

Question 6. The power of a pump is 1 kW means that the pump can perform 1000 J work in 1 s.

Answer: True

## Chapter 5 Power Numerical Examples

**Useful Information**

- If W amount of work in done in time t, then W power P = \(\frac{W}{t}\).
- If the force applied on a body moving with velocity v be F then, power P = F x v
- If m mass is lifted to a height h against gravity in time t then power P = \(\frac{mgh}{t}\)

**Question 1. How much energy is required to lift 200 L of water every minute to a height of 15 m ? [Mass of 1L of water is 1 kg]**

**Answer:**

Mass of 200 L of water, m = 200 kg

Work W to be done to raise 200 kg of water to h = 15 m against gravity, W = mgh

Time, t = 1 min (=60 s) is required to do this work.

∴ power, P = \(\frac{W}{t}\) = \(\frac{mgh}{t}\)

= \(\frac{200 \times 9.8 \times 15}{60}\) J/s = 490 w

**Question 2. The power of a man is 6W. How much work does he perform in 10 minute?**

**Answer:**

Power of the person P = 6W, time to do work t= 10 x 60 = 600s

∴ Work done by the person W = P x t =6 X 600 = 3600 J

**Question 3. A boy of mass 30 kg can go up 20 steps, each of height 10 cm, in 25 s. Calculate the power of the boy.**

**Answer:**

Mass of the boy, m = 30 kg

So, his weight = mg = 30 x 9.8 N

Height of 20 steps,

h = 10 x 20 cm = 200 cm = 2m

Work done by the boy,

W = mgh =30 x 9.8 x 2J = 588 J

This amount of work is done in t = 25 s

∴ power of the boy,

P = \(\frac{W}{t}\) = \(\frac{588}{25}\)J/s = 23.52W

**Question 4. The power of a dump is 2kW. How much time does it take to fill up a tank of 800 L capacity kept at a height of 12 m with its help? [Mass of 1 L of water is 1 kg]**

**Answer:**

Power of the pump, P = 2 kW = 2000 W

Mass of 800 L of water = 800 kg

Work done to raise a mass of m = 800 kg to a height of h = 12 m against gravity,

W = mgh = 800 x 9.8 x 12J

∴ if t time is required to fill up the tank, then

t = \(\frac{W}{p}=\frac{800 \times 9.8 \times 12}{2000}=47.04 \mathrm{~s}\)

**Question 5. A pump is lifting 600 kg of water per minute to a height of 20 m. If the efficiency of the pump is 80%, what is its power?**

**Answer:**

Suppose, power of the pump = P

Efficiency of the pump =80%

∴ effective power of the pump,

\(P_1=\frac{80}{100} P=0.8 P\)With the help of the pump, a mass (m) of 600 kg of water is raised to a height of h = 20 m in t = 1 min = 60s.

So, \(P_1=\frac{m g h}{t} \text { or, } 0.8 P=\frac{m g h}{t} \text { or, } P=\frac{m g h}{0.8 t}\)

∴ P = \(\frac{600 \times 9.8 \times 20}{0.8 \times 60}=2450 \mathrm{~W}=2.45 \mathrm{~kW}\)

**Question 6. A car is moving on a rough horizontal road with a uniform velocity. Friction of the road is 200 N and the power of the engine is 2 kW. Calculate the velocity of the car in km/h units.**

**Answer:**

Friction of the road, F = 200 N

Power of the engine, P = 2 kW = 2000 W

Suppose, velocity of the car = v

So, P = f x v

∴ v = \(\frac{P}{F}=\frac{2000}{200}=10 \mathrm{~m} / \mathrm{s}\)

= \(10 \times \frac{18}{5} \mathrm{~km} / \mathrm{h}\)

[1 m/s = 18/5 km/h]

= \(36 \mathrm{~km} / \mathrm{h}\)

**Question 7. A motor car moves with velocity 36 km/h by applying an average force of 20N. Find power of the car.**

**Answer:**

Velocity of the car,

v = 36 km/h = \(\frac{36000 \mathrm{~m}}{3600 \mathrm{~s}}\) = 10 m/s

Force applied by the car F = 20 N

∴ the power of the car P = F x v = 20 x 10 = 200 W

**Question 8. The work done by a human heart is 11 per beat. Calculate power of the heart if it beats 72 times in a minute.**

**Answer:**

Work done by the heart in 72 beats

W = 1 x 72 = 72 J

∴ power of the heart

P = \(\frac{W}{t}=\frac{72 \mathrm{~J}}{60 \mathrm{~s}}=1.2 \mathrm{~W}\)