- Dr.Sanjaykumar Pawar
Gravitational Potential Energy Notes for NEET with Formula & Examples
 |
| Gravitational Potential Energy (PE = mgh) and its conversion into kinetic energy explained with simple examples for NEET students. |
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NEET Physics Notes - Chapter 5.7 The Concept of Potential Energy
NEET Physics Notes
Chapter 5.7 – The Concept of Potential Energy
1. Meaning of Potential Energy
The word Potential means the ability or capacity to do work in the future.
Potential Energy (PE) is the energy stored in a body because of its position or shape (configuration).
Definition
Potential Energy is the energy possessed by a body due to its position or configuration.
2. Everyday Examples
Example 1 – Stretched Bow
- A stretched bow stores energy.
- When the string is released, stored energy changes into kinetic energy.
- The arrow moves with high speed.
Example 2 – Earthquake
- The Earth's crust has cracks called fault lines.
- These fault lines store a large amount of energy.
- When they suddenly move, the stored energy is released.
- This causes an earthquake.
Potential Energy is stored energy that can later change into kinetic energy.
3. Gravitational Potential Energy
Consider a ball of mass m near the Earth's surface.
Assumption
- Acceleration due to gravity (g) remains constant.
- Height (h) is much smaller than Earth's radius.
\[
h \ll R_E
\]
Where
- h = height of object
- RE = radius of Earth
4. Raising a Ball
Suppose a ball is lifted upward through height h.
- Gravity acts downward.
- An external force is required to lift the ball.
- Work is done against gravity.
\[
W = mgh
\]
This work gets stored as gravitational potential energy.
5. Formula of Gravitational Potential Energy
\[
PE = V(h)=mgh
\]
Where
- m = mass
- g = acceleration due to gravity
- h = height
6. Important Points
- Greater height → Greater Potential Energy.
- Greater mass → Greater Potential Energy.
- If h = 0, then Potential Energy = 0.
7. Relation Between Force and Potential Energy
\[
F=-\frac{dV}{dh}
\]
Since
\[
V=mgh
\]
Differentiate,
\[
\frac{dV}{dh}=mg
\]
Therefore,
\[
F=-mg
\]
The negative sign shows that gravity always acts downward.
8. Conversion of Potential Energy into Kinetic Energy
When the ball is released:
- Potential Energy decreases.
- Kinetic Energy increases.
- At the ground, Potential Energy becomes minimum.
- Kinetic Energy becomes maximum.
9. Speed of Falling Ball
Using the equation of motion,
\[
v^2=u^2+2gh
\]
Since
\[
u=0
\]
Therefore,
\[
v^2=2gh
\]
10. Kinetic Energy at Ground
\[
KE=\frac12 mv^2
\]
Substitute
\[
v^2=2gh
\]
\[
KE=\frac12 m(2gh)
\]
\[
KE=mgh
\]
Hence,
\[
PE=KE
\]
11. When Does Potential Energy Exist?
Potential Energy exists only for Conservative Forces.
Examples
- Gravitational Force
- Spring Force
- Electrostatic Force
12. Conservative Force
A Conservative Force is a force whose work depends only on the initial and final positions and not on the path followed.
Examples
- Gravity
- Spring Force
- Electrostatic Force
13. Mathematical Definition
\[
F(x)=-\frac{dV}{dx}
\]
Potential Energy exists only if the force satisfies this equation.
14. Work Done by Conservative Force
\[
\int_{x_i}^{x_f}F(x)\,dx
=-(V_f-V_i)
\]
or
\[
W=V_i-V_f
\]
Meaning:
Work done by a conservative force equals the decrease in Potential Energy.
15. Change in Potential Energy
\[
\Delta V=-W
\]
Meaning
- If gravity does positive work, Potential Energy decreases.
- If work is done against gravity, Potential Energy increases.
16. Inclined Plane Example
A body slides from the top of a smooth inclined plane of height h.
Its speed at the bottom is
\[
v=\sqrt{2gh}
\]
This speed depends only on height and not on the angle of inclination.
17. Kinetic Energy at Bottom
\[
KE=\frac12 mv^2
\]
Substitute
\[
v^2=2gh
\]
\[
KE=mgh
\]
Hence,
Loss of Potential Energy = Gain of Kinetic Energy
18. Non-Conservative Force
A Non-Conservative Force is a force whose work depends on the path followed.
Examples
- Friction
- Air Resistance
- Viscous Force
19. Dimensions of Potential Energy
\[
[ML^2T^{-2}]
\]
20. SI Unit
Joule (J)
21. Energy Conversion
Potential Energy can convert into
- Kinetic Energy
- Heat Energy
- Sound Energy
22. Important NEET Formula Sheet
| Formula |
Expression |
| Gravitational Potential Energy |
\(PE=mgh\) |
| Force and Potential Energy |
\(F=-\frac{dV}{dh}\) |
| General Relation |
\(F=-\frac{dV}{dx}\) |
| Work Done |
\(W=V_i-V_f\) |
| Change in Potential Energy |
\(\Delta V=-W\) |
| Speed of Falling Body |
\(v=\sqrt{2gh}\) |
| Kinetic Energy |
\(KE=\frac12 mv^2\) |
| At Ground |
\(KE=mgh\) |
23. NEET One-Line Revision
- Potential Energy is stored energy.
- It depends on position or configuration.
- Gravitational Potential Energy = mgh.
- Gravity is a conservative force.
- \(F=-\frac{dV}{dx}\)
- \(\Delta V=-W\)
- Potential Energy decreases when gravity does work.
- Potential Energy converts into Kinetic Energy during free fall.
- On a frictionless inclined plane, speed depends only on height.
- SI Unit = Joule (J).
- Dimensions = \([ML^2T^{-2}]\)
- Mechanical Energy remains conserved when only conservative forces act.
CBSE Class 11 Physics - Chapter 5.7 Question Bank (Part 1)
CBSE Class 11 Physics
Chapter 5.7 – The Concept of Potential Energy
Part 1 : MCQs & Very Short Answer Questions
Section A : Multiple Choice Questions (MCQs)
1. Potential energy is the energy possessed by a body due to its:
- Speed
- Mass
- Position or configuration
- Temperature
Answer: (c) Position or configuration
2. The SI unit of potential energy is:
- Newton
- Joule
- Watt
- Pascal
Answer: (b) Joule
3. Gravitational potential energy of a body is:
- mg
- gh
- mgh
- mv²
Answer: (c) mgh
4. The dimensional formula of potential energy is:
- [MLT⁻²]
- [ML²T⁻²]
- [ML²T⁻¹]
- [MLT]
Answer: (b) [ML²T⁻²]
5. Potential energy depends upon:
- Speed
- Position or configuration
- Momentum
- Temperature
Answer: (b) Position or configuration
6. Which of the following is a conservative force?
- Friction
- Air resistance
- Gravity
- Viscous force
Answer: (c) Gravity
7. The relation between force and potential energy is:
- F = dV/dx
- F = –dV/dx
- F = V/x
- F = Vx
Answer: (b) F = –dV/dx
8. If the height of an object is doubled, its gravitational potential energy becomes:
- Half
- Double
- Four times
- Zero
Answer: (b) Double
9. At ground level, the potential energy is generally taken as:
- Infinity
- mgh
- Zero
- mg
Answer: (c) Zero
10. During free fall:
- Potential energy increases
- Kinetic energy decreases
- Potential energy converts into kinetic energy
- Both energies remain constant
Answer: (c) Potential energy converts into kinetic energy
Section B : Very Short Answer Questions (1 Mark)
1. Define potential energy.
Potential energy is the energy possessed by a body due to its position or configuration.
2. Write the SI unit of potential energy.
Joule (J)
3. Write the dimensional formula of potential energy.
[ML²T⁻²]
4. Write the formula of gravitational potential energy.
PE = mgh
5. What is a conservative force?
A conservative force is a force whose work depends only on the initial and final positions and not on the path followed.
6. Name one conservative force.
Gravitational force.
7. Name one non-conservative force.
Frictional force.
8. Write the relation between force and potential energy.
F = –dV/dx
9. What is gravitational potential energy?
It is the energy possessed by a body due to its position above the Earth's surface.
10. What happens to potential energy during free fall?
Potential energy decreases and converts into kinetic energy.
11. Write the expression for kinetic energy.
KE = ½mv²
12. State the law of conservation of mechanical energy.
When only conservative forces act on a body, the total mechanical energy (Potential Energy + Kinetic Energy) remains constant.
13. Give one example of stored energy.
A stretched spring or a stretched bow.
14. Does potential energy depend upon velocity?
No. It depends only on position or configuration.
15. Write the mathematical relation for change in potential energy.
ΔV = –W
CBSE Class 11 Physics - Chapter 5.7 Question Bank (Part 2)
CBSE Class 11 Physics
Chapter 5.7 – The Concept of Potential Energy
Part 2 : Short Answer & Long Answer Questions
Section C : Short Answer Questions (2–3 Marks)
1. Define potential energy. Explain with one example.
Potential energy is the energy possessed by a body due to its position or configuration.
Example:
A stretched bow stores potential energy. When the string is released, the stored potential energy changes into kinetic energy and the arrow moves with high speed.
2. Derive the expression for gravitational potential energy.
Consider a body of mass
m lifted vertically through a height
h.
Weight of body = mg
Work done against gravity
W = Force × Distance
W = mg × h
W = mgh
This work is stored as gravitational potential energy.
Therefore,
PE = mgh
3. Why is gravitational force called a conservative force?
Gravitational force is called a conservative force because:
- Its work depends only on the initial and final positions.
- It does not depend on the path followed.
- Mechanical energy remains conserved when only gravity acts.
4. What happens to potential energy during free fall?
During free fall:
- Potential energy decreases.
- Kinetic energy increases.
- Total mechanical energy remains constant.
Thus, potential energy is converted into kinetic energy.
5. Differentiate between conservative and non-conservative forces.
| Conservative Force |
Non-Conservative Force |
| Work depends only on initial and final positions. |
Work depends on the path followed. |
| Mechanical energy is conserved. |
Mechanical energy is not conserved. |
| Example: Gravity |
Example: Friction |
6. Explain the relation between force and potential energy.
For a conservative force,
\[
F=-\frac{dV}{dx}
\]
The negative sign shows that the force acts in the direction of decreasing potential energy.
Section D : Long Answer Questions (5 Marks)
1. Explain gravitational potential energy and derive its formula.
Potential energy is the stored energy possessed by a body because of its position.
Suppose a body of mass
m is lifted vertically upward through height
h.
Weight of the body
Force = mg
Work done
W = Force × Distance
W = mg × h
W = mgh
Since this work is stored as energy,
PE = mgh
Where
- m = Mass of the body
- g = Acceleration due to gravity
- h = Height above the ground
Therefore,
Gravitational Potential Energy = mgh
2. Explain how potential energy converts into kinetic energy during free fall.
Consider a body kept at a height
h.
Initially,
Potential Energy = mgh
When the body is released,
- Potential energy decreases.
- Kinetic energy increases.
- Total mechanical energy remains constant.
Using the equation of motion,
\[
v^2=2gh
\]
Kinetic energy,
\[
KE=\frac12 mv^2
\]
Substituting,
\[
KE=\frac12 m(2gh)
\]
\[
KE=mgh
\]
Hence,
Potential Energy = Kinetic Energy
This proves the conservation of mechanical energy.
3. Explain the law of conservation of mechanical energy.
The law states:
"When only conservative forces act on a body, the total mechanical energy remains constant."
Mechanical Energy
Mechanical Energy = Potential Energy + Kinetic Energy
During free fall,
- Potential energy decreases.
- Kinetic energy increases.
- The total remains constant.
Therefore,
PE + KE = Constant
This is known as the law of conservation of mechanical energy.
4. A body of mass 5 kg is lifted to a height of 10 m. Calculate its gravitational potential energy. (Take g = 9.8 m/s²)
Given:
- Mass (m) = 5 kg
- Height (h) = 10 m
- g = 9.8 m/s²
Formula
PE = mgh
Calculation
PE = 5 × 9.8 × 10
PE = 490 J
Answer: The gravitational potential energy is
490 J.
5. State any five characteristics of potential energy.
- Potential energy is stored energy.
- It depends on position or configuration.
- Its SI unit is Joule (J).
- Its dimensional formula is [ML²T⁻²].
- It can be converted into kinetic energy.
CBSE Class 11 Physics - Chapter 5.7 Question Bank (Part 3)
CBSE Class 11 Physics
Chapter 5.7 – The Concept of Potential Energy
Part 3 : Assertion & Reason, Fill in the Blanks, Statement-Based Questions
Section E : Assertion and Reason Questions
Question 1
Assertion (A): Gravity is a conservative force.
Reason (R): Work done by gravity depends only on the initial and final positions.
Answer:
✔ Assertion is True.
✔ Reason is True.
✔ Reason is the correct explanation of the Assertion.
Question 2
Assertion (A): Potential energy decreases during free fall.
Reason (R): Kinetic energy increases during free fall.
Answer:
✔ Assertion is True.
✔ Reason is True.
✔ Reason correctly explains the Assertion.
Question 3
Assertion (A): Friction is a conservative force.
Reason (R): Work done by friction depends upon the path followed.
Answer:
✘ Assertion is False.
✔ Reason is True.
Question 4
Assertion (A): SI unit of potential energy is Joule.
Reason (R): Potential energy is a form of energy and work.
Answer:
✔ Assertion is True.
✔ Reason is True.
✔ Reason correctly explains the Assertion.
Question 5
Assertion (A): Potential energy depends upon velocity.
Reason (R): Potential energy depends upon position.
Answer:
✘ Assertion is False.
✔ Reason is True.
Section F : Fill in the Blanks
1. Potential energy depends upon the __________ of the body.
Answer: Position
2. The SI unit of potential energy is __________.
Answer: Joule (J)
3. Gravitational potential energy is equal to __________.
Answer: mgh
4. Gravity is a __________ force.
Answer: Conservative
5. Friction is a __________ force.
Answer: Non-conservative
6. During free fall, potential energy converts into __________ energy.
Answer: Kinetic
7. The dimensions of potential energy are __________.
Answer: [ML²T⁻²]
8. The relation between force and potential energy is __________.
Answer: F = −dV/dx
9. Potential energy is also called __________ energy.
Answer: Stored
10. Mechanical energy remains constant when only __________ forces act.
Answer: Conservative
Section G : Statement-Based Questions (True / False)
State whether the following statements are True or False.
- Potential energy depends upon position.
Answer: True
- Friction is a conservative force.
Answer: False
- SI unit of potential energy is Joule.
Answer: True
- Potential energy can be converted into kinetic energy.
Answer: True
- Gravity is a conservative force.
Answer: True
- Potential energy depends upon velocity.
Answer: False
- Mechanical energy is conserved when only conservative forces act.
Answer: True
- The dimensional formula of potential energy is [ML²T⁻²].
Answer: True
- Potential energy is measured in Newton.
Answer: False
- A stretched spring possesses potential energy.
Answer: True
Section H : Formula-Based Questions
1. Write the formula of gravitational potential energy.
PE = mgh
2. Write the relation between force and potential energy.
F = −dV/dx
3. Write the formula for change in potential energy.
ΔV = −W
4. Write the formula of kinetic energy.
KE = ½mv²
5. Write the speed of a freely falling body from height h.
v = √(2gh)
CBSE Class 11 Physics - Chapter 5.7 Question Bank (Part 4)
CBSE Class 11 Physics
Chapter 5.7 – The Concept of Potential Energy
Part 4 : Case Study, Match the Columns, Competency-Based Questions & HOTS
Section I : Case Study Questions
Case Study
A ball of mass 2 kg is lifted vertically to a height of
10 m. It is then released and falls freely under gravity.
Take g = 9.8 m/s².
Answer the following questions.
1. What type of energy does the ball possess at the highest point?
Potential Energy.
2. Calculate the gravitational potential energy of the ball.
Given:
Mass = 2 kg
Height = 10 m
g = 9.8 m/s²
PE = mgh
= 2 × 9.8 × 10
= 196 J
Answer: 196 J
3. What happens to the potential energy during free fall?
Potential energy decreases continuously.
4. Which form of energy increases during free fall?
Kinetic Energy.
5. Which law is verified in this example?
Law of Conservation of Mechanical Energy.
Section J : Match the Columns
| Column A |
Column B |
| 1. Potential Energy |
A. Joule |
| 2. Kinetic Energy |
B. Energy of Motion |
| 3. Gravity |
C. Conservative Force |
| 4. Friction |
D. Non-Conservative Force |
| 5. SI Unit of Potential Energy |
E. Stored Energy |
Correct Matching
| Column A |
Column B |
| 1 |
E |
| 2 |
B |
| 3 |
C |
| 4 |
D |
| 5 |
A |
Section K : Competency-Based Questions
1. Why does a book kept on a table possess potential energy?
Because it is at a height above the ground and has the ability to do work if allowed to fall.
2. Why is no work done in moving a body horizontally on a frictionless surface?
Because the height of the body does not change. Therefore, gravitational potential energy remains constant.
3. Why does a stretched spring possess potential energy?
Because energy is stored due to the change in its shape (configuration).
4. Why does an object gain kinetic energy while falling?
Because its gravitational potential energy is converted into kinetic energy during free fall.
5. Why is gravity considered a conservative force?
Because the work done by gravity depends only on the initial and final positions, not on the path followed.
Section L : HOTS (Higher Order Thinking Skills)
1. Can a body have potential energy even when it is at rest? Explain.
Yes. A body at rest can possess potential energy due to its position or configuration. For example, a book placed on a shelf has gravitational potential energy.
2. Why does the speed of a body at the bottom of a smooth inclined plane not depend on the angle of inclination?
Because the loss of potential energy depends only on the vertical height. Hence, the final kinetic energy and speed depend only on height, not on the angle of inclination.
3. Explain why friction cannot store potential energy.
Friction is a non-conservative force. The work done against friction is converted into heat and sound energy instead of being stored as potential energy.
4. A body is lifted to two different heights. At which height will its potential energy be greater? Why?
The potential energy will be greater at the larger height because gravitational potential energy is directly proportional to height (PE = mgh).
5. Give one practical example showing the conversion of potential energy into kinetic energy.
A roller coaster at the top of a track has maximum potential energy. As it moves downward, its potential energy is converted into kinetic energy, increasing its speed.
Section M : Extra Practice Questions
- State the principle of conservation of mechanical energy.
- Write any two examples of conservative forces.
- Write any two examples of non-conservative forces.
- Explain why potential energy is called stored energy.
- Write the SI unit and dimensional formula of potential energy.
Answers:
- Total mechanical energy remains constant when only conservative forces act.
- Gravitational force and spring force.
- Frictional force and air resistance.
- Because it is stored due to position or configuration and can later convert into kinetic energy.
- SI Unit: Joule (J), Dimensional Formula: [ML²T⁻²]
