Learn Chapter 5: Work, Energy, and Power from the new Physics syllabus for 9th class. Explore solved exercises with detailed explanations and tips to excel in your exams.
Question 5.1
Statement: Work done is maximum when the angle between the force F and the displacement d is:
Options:
(a) 0∘
(b) 30∘
(c) 60∘
(d) 90∘
Answer: (a) 0∘
Explanation:
The work done is given by the formula: W=Fdcosθ
The cosine function is maximum when θ=0∘ because cos0∘=1. Thus, work done is maximum when the force and displacement are in the same direction.
Tip: Memorize that cosθ decreases as the angle increases from 0∘ to 90∘. For θ=90∘, work done becomes zero.
Question 5.2
Statement: A joule can also be written as:
Options:
(a) kg m2s−2
(b) kg m s−1
(c) kg m−2s−2
(d) kg m s−2
Answer: (a) kg m2s−2
Explanation:
A joule is the unit of energy or work, given as: Work=Force×Displacement
Force is measured in kg m s−2, and displacement in meters . Therefore, Joule=(kg m s−2)×m=kg m2s−2.
Tip: Remember that joules involve mass, distance squared, and time squared in their derived units.
Question 5.3
Statement: The SI unit of power is:
Options:
(a) joule
(b) newton
(c) watt
(d) second
Answer: (c) watt
Explanation:
Power is the rate at which work is done or energy is transferred. It is defined as: P=W/t
Where P is power in watts, W is work in joules, and t is time in seconds.
Tip: Memorize key SI units: work (joule), force (newton), and power (watt).
Question 5.4
Statement: The power of a water pump is 2 kW. The amount of water it can raise in one minute to a height of 5 m is:
Options:
(a) 1000 litres
(b) 1200 litres
(c) 2000 litres
(d) 2400 litres
Answer: (d) 2400 litres
Explanation:
The power of the pump is P=2000 WP . Work is given by: W=mgh
Where mm is mass, g=9.8 m/s2, and h=5 m. Power is work done per second: P=mgh/t
Rearranging for mm: m=P⋅t/gh=2000×60/9.8×5=240 kg
Since 1 kg of water equals 1 litre, the answer is 2400 litres.
Tip: Always use consistent units and formulas for work, power, and time.
Question 5.5
Statement: A bullet of mass 0.05 kg has a speed of 300 m/s. Its kinetic energy will be:
Options:
(a) 2250 J
(b) 4500 J
(c) 1500 J
(d) 1125 J
Answer: (b) 4500 J
Explanation:
Kinetic energy is given by: KE=1/2mv2
Substitute m=0.05 kg and v=300 m/s
KE=1/2×0.05×(300)2=4500 J
Tip: Remember to square the velocity in the formula.
Question 5.6
Statement: If a car doubles its speed, its kinetic energy will be:
Options:
(a) the same
(b) increased four times
(c) increased two times
(d) reduced two times
Answer: (b) increased four times
Explanation:
Kinetic energy depends on the square of velocity: KE∝v2
If the speed doubles (v→2v), the kinetic energy becomes: KE∝(2v)2=4v2.
Tip: Always relate proportionality with squared terms in energy calculations.
Question 5.7
Statement: The energy possessed by a body by virtue of its position is:
Options:
(a) kinetic energy
(b) potential energy
(c) chemical energy
(d) solar energy
Answer: (b) potential energy
Explanation:
Potential energy is the energy stored in an object due to its position in a gravitational field, given by: PE=mgh
Tip: Potential energy depends on height, while kinetic energy depends on motion.
Question 5.8
Statement: The magnitude of momentum of an object is doubled; the kinetic energy of the object will:
Options:
(a) double
(b) increase to four times
(c) reduce to one-half
(d) remain the same
Answer: (b) increase to four times
Explanation:
Momentum (pp) is related to kinetic energy (KE) as:
KE=p2/2m
If momentum doubles (p→2p)
KE∝(2p)2=4p2
Tip: Understand the relationship between momentum and kinetic energy.
Question 5.9
Statement: Which of the following is not renewable energy?
Options:
(a) Hydro-electric energy
(b) Fossil fuels
(c) Wind energy
(d) Solar energy
Answer: (b) Fossil fuels
Explanation:
Fossil fuels (coal, oil, natural gas) take millions of years to form and are not renewable. Renewable energy sources like solar, wind, and hydro are replenished naturally.
Tip: Fossil fuels are non-renewable because their reserves are finite.
Here are the solutions to the short answer and constructed response questions with clear and simple explanations:
Short Answer Questions (Part B)
Question 5.1
What is the work done on an object that remains at rest when a force is applied to it?
Answer:
The work done is zero.
Explanation:
Work is given by the formula: W=F⋅d⋅cosθ
Since the object remains at rest, the displacement d=0. Therefore, work W=0.
Question 5.2
A slow-moving car may have more kinetic energy than a fast-moving motorcycle. How is this possible?
Answer:
Kinetic energy depends on both mass and velocity: KE=1/2mv2
If the car is very heavy (large m) and the motorcycle is light (small m), the car’s kinetic energy can be greater even if it moves slowly.
Question 5.3
A force F1 does 5 J of work in 10 s. Another force F2 does 3 J of work in 5 s. Which force delivers greater power?
Answer:
Power is given by: P=W/t
For F1: P1=5/10=0.5 W
For F2: P2=3/5=0.6 W
Thus, F2 delivers greater power.
Question 5.4
A woman runs up a flight of stairs. The gain in her gravitational potential energy is 4500 J. If she runs up the stairs with twice the speed, what will be her gain in potential energy?
Answer:
The gain in potential energy will still be 4500 J.
Explanation:
Potential energy depends only on height (PE=mgh), not on speed. Running faster does not change the height.
Question 5.5
Define work and its SI unit.
Answer:
Work is done when a force moves an object in the direction of the force. Mathematically: W=F⋅d⋅cosθ
The SI unit of work is the joule (J).
Question 5.6
What is the potential energy of a body of mass mm when it is raised through a height hh?
Answer:
Potential energy is given by: PE=mgh
Where:
- m = mass of the body
- g = gravitational acceleration (9.8 m/s2)
- h = height
Question 5.7
Find an expression for the kinetic energy of a moving body.
Answer:
Kinetic energy is given by: KE=1/2mv2
Where:
- m = mass of the body
- v = velocity of the body
Question 5.8
Define the efficiency of a working system. Why can a system not have 100% efficiency?
Answer:
Efficiency is the ratio of useful energy output to the total energy input: Efficiency=Useful Energy Output/Total Energy Input ×100
No system can have 100%100\% efficiency because some energy is always lost as heat, sound, or friction.
Question 5.9
What is power? Define the unit used for it.
Answer:
Power is the rate at which work is done or energy is transferred: P=W/t
The SI unit of power is the watt (W).
Question 5.10
Differentiate between renewable and non-renewable energy sources.
Answer:
- Renewable energy: Can be replenished naturally, e.g., solar, wind, and hydro energy.
- Non-renewable energy: Exists in limited quantities and cannot be replenished, e.g., fossil fuels (coal, oil).
Constructed Response Questions (Part C)
Question 5.1
Can the kinetic energy of a body ever be negative?
Answer:
No, kinetic energy cannot be negative.
Explanation:
Kinetic energy is given by KE=1/2mv2. Since both mass (m) and the square of velocity (v2) are always positive, KE is always positive.
Question 5.2
Which one has the greater kinetic energy: an object traveling with a velocity vv or an object twice as heavy traveling with a velocity of v2\frac{v}{2}?
Answer:
Let the mass of the first object be mm, so KE1=1/2mv2
The second object has mass 2m and velocity v2
KE2=1/2(2m)(v2)/2=1/2(2m)⋅v2/4=mv2/4
Thus, KE1>KE2.
Question 5.3
A car is moving along a curved road at constant speed. Does its kinetic energy change?
Answer:
No, the kinetic energy does not change.
Explanation:
Kinetic energy depends on speed, not direction. Since the speed is constant, the kinetic energy remains the same.
Question 5.4
Comment on the statement: “An object has one joule of potential energy.”
Answer:
The statement means the object’s potential energy is equal to the work done in lifting it to a certain height where: PE=1 J.
Question 5.5
While driving on a motorway, the tyre of a vehicle sometimes bursts. What may be its cause?
Answer:
A tyre may burst due to:
- Overheating from friction.
- Excessive air pressure.
- Damage from sharp objects.
Question 5.6
While playing cricket, a ball smashes a windowpane. Describe the energy changes in this event.
Answer:
- The ball has kinetic energy while in motion.
- Upon impact, the ball transfers energy to the windowpane, causing it to break.
- Some energy is lost as sound and heat.
Question 5.7
A man rows a boat upstream at rest with respect to the shore. Is he doing work?
Answer:
No, he is not doing work with respect to the shore because there is no displacement.
Question 5.8
A cyclist goes downhill from the top of a steep hill without pedaling and takes it to the top of the next hill. Draw a diagram of what happened.
Answer:
The cyclist’s gravitational potential energy at the top of the first hill converts to kinetic energy as he descends, then converts back to potential energy as he climbs the next hill. A diagram would show a curved path between two hills.
