Conservation of Mechanical Energy Class 11 Notes, MCQs, Questions & Answers | CBSE & NEET

-  Dr Sanjay Kumar Pawar 

Conservation of Mechanical Energy Class 11 Physics Notes PDF | CBSE & NEET 

Conservation of Mechanical Energy explained with a falling ball showing the conversion of potential energy into kinetic energy.

Internal Links

Link this page to related Class 11 Physics topics to improve SEO and user navigation:

1. Work, Energy and Power Class 11 Notes
2. Work-Energy Theorem Explained
3. Potential Energy Class 11 Notes
4. Kinetic Energy Formula and Examples
5. Conservative and Non-Conservative Forces
6. Gravitational Potential Energy Notes
7. Free Fall Motion Class 11
8. Laws of Motion Class 11
9. Newton's Laws of Motion Notes
10. Circular Motion Class 11 Notes
11. System of Particles and Rotational Motion
12. Gravitation Class 11 Notes
13. Mechanical Properties of Solids
14. Complete Class 11 Physics Notes Index 
15. Class 11 Physics MCQs with Answers
16. CBSE Class 11 Physics Important Questions
17. NEET Physics Chapter-wise Notes
18. NCERT Solutions for Class 11 Physics
19. Class 11 Physics Formula Sheet
20. Previous Year CBSE Class 11 Physics Questions

Chapter 5.8
Conservation of Mechanical Energy

Definition:
Mechanical Energy is the sum of Kinetic Energy (KE) and Potential Energy (PE).

Mechanical Energy = KE + PE

1. Work-Energy Theorem

Suppose a body moves through a small distance Δx under the action of force F. According to the Work-Energy Theorem,

ΔK = F(x) Δx

This means the work done by a force changes the kinetic energy of the body.

• Positive work increases kinetic energy.
• Negative work decreases kinetic energy.

2. Conservative Force

If the force is conservative, then potential energy can be defined.

−ΔU = F(x) Δx

The negative sign shows that whenever potential energy decreases, kinetic energy increases.

Example:
A falling stone loses potential energy and gains kinetic energy.

3. Combining the Equations

From the two equations:

ΔK = −ΔU

Therefore,

ΔK + ΔU = 0

or

Δ(K + U) = 0

4. Conservation of Mechanical Energy

Since Δ(K+U)=0, the total mechanical energy never changes.

K + U = Constant

This is called the Law of Conservation of Mechanical Energy.

5. Equation Between Two Positions

Ki + Ui = Kf + Uf

The total mechanical energy before motion equals the total mechanical energy after motion.

6. Conservative Force - Important Properties

• Potential energy can be defined.
• Work depends only on initial and final positions.
• Work does not depend on the path.
• Work done in a closed path is zero.
• Mechanical energy remains conserved.

7. Example - Falling Ball

A ball of mass m is dropped from height H. Initially the velocity is zero.

At Height H

PE = mgH

KE = 0

EH = mgH

At Height h

PE = mgh

KE = ½mv²h

Eh = mgh + ½mv²h

At Ground Level

PE = 0

KE = ½mv²f

E0 = ½mv²f

8. Conservation of Energy

EH = Eh = E0

Since only gravity acts on the body, mechanical energy remains constant.

mgH = mgh + ½mv²h = ½mv²f

9. Final Velocity

Using conservation of energy,

mgH = ½mv²f

After simplifying,

vf = √(2gH)

10. Velocity at Height h

mgH = mgh + ½mv²h

Therefore,

vh² = 2g(H − h)

11. Energy Conversion

Position	Potential Energy	Kinetic Energy
Top	Maximum	Zero
Middle	Decreasing	Increasing
Ground	Zero	Maximum

12. Important Points for NEET

• Mechanical Energy = KE + PE
• Gravity is a conservative force.
• Spring force is also conservative.
• Mechanical energy remains constant if only conservative forces act.
• Work done by a conservative force depends only on the initial and final positions.
• Work done in a closed path is zero.
• At the highest point, PE is maximum and KE is zero.
• At the ground, KE is maximum and PE is zero.
• Potential energy converts into kinetic energy during free fall.

13. Formula Sheet

Mechanical Energy = KE + PE

ΔK + ΔU = 0

K + U = Constant

Ki + Ui = Kf + Uf

PE = mgh

KE = ½mv²

vf = √(2gH)

vh² = 2g(H − h)

Work done in a Closed Path = 0

Prepared for NEET Physics Students • Chapter 5.8 - Conservation of Mechanical Energy

Conservation of Mechanical Energy

What is Mechanical Energy?

Mechanical Energy is the sum of Kinetic Energy (KE) and Potential Energy (PE).

Mechanical Energy = KE + PE

Work-Energy Theorem

When a force acts on an object, its kinetic energy changes.

ΔKE = Work Done

For conservative forces, Potential Energy decreases when Kinetic Energy increases.

ΔKE + ΔPE = 0

Energy Conversion During Falling

Top
PE Maximum
KE Zero

Middle
PE ↓
KE ↑

Ground
PE Zero
KE Maximum

Visual Falling Ball

⬇

As the ball falls, Potential Energy continuously converts into Kinetic Energy.

Example

Position	Potential Energy	Kinetic Energy	Total Energy
Top	100 J	0 J	100 J
Middle	60 J	40 J	100 J
Ground	0 J	100 J	100 J

Important Formulae

PE = mgh

KE = ½mv²

KE + PE = Constant

vf = √(2gH)

vh² = 2g(H − h)

NEET Remember:

• Gravity is a conservative force.
• Total Mechanical Energy remains constant if only conservative forces act.
• At the highest point: PE is maximum and KE is zero.
• At the ground: KE is maximum and PE is zero.
• Potential Energy converts into Kinetic Energy during falling.

CBSE Class 11 Physics

Chapter 5.8 - Conservation of Mechanical Energy

Question Bank with Answers

---

Part A - Multiple Choice Questions

1. Mechanical energy is the sum of

1. Potential energy and Heat energy
2. Kinetic energy and Potential energy
3. Heat energy and Electrical energy
4. Sound energy and Potential energy

Answer: B

2. Mechanical energy remains constant when

1. Friction acts
2. Air resistance acts
3. Only conservative forces act
4. External force acts

Answer: C

3. Which one is a conservative force?

1. Friction
2. Gravity
3. Air resistance
4. Viscous force

Answer: B

4. Work done by a conservative force depends on

1. Path followed
2. Distance travelled
3. Initial and final positions only
4. Speed

Answer: C

5. Work done in a closed path by gravity is

1. Positive
2. Negative
3. Zero
4. Infinite

Answer: C

---

Part B - Very Short Answer Questions

1. Define mechanical energy.

Answer: Mechanical energy is the sum of kinetic energy and potential energy.

2. Write the formula of mechanical energy.

Answer: E = KE + PE

3. Name one conservative force.

Answer: Gravitational force.

4. Write the formula of kinetic energy.

Answer: KE = ½mv²

5. Write the formula of potential energy.

Answer: PE = mgh

---

Part C - Short Answer Questions

1. What is conservation of mechanical energy?

Answer:
When only conservative forces act on a body, the total mechanical energy (kinetic energy + potential energy) remains constant throughout the motion.

2. What is a conservative force?

Answer:
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

---

Part D - Long Answer Questions

1. State the law of conservation of mechanical energy.

Answer:
If only conservative forces act on a body, its total mechanical energy remains constant. Mechanical Energy = Kinetic Energy + Potential Energy Initial Energy Ki + Ui Final Energy Kf + Uf Therefore, Ki + Ui = Kf + Uf Example: A freely falling body loses potential energy and gains kinetic energy. The total mechanical energy remains constant.

---

Part E - Assertion and Reason

Assertion: Mechanical energy remains constant when only conservative forces act.

Reason: Gravity is a conservative force.

Answer: Both Assertion and Reason are true, and Reason is the correct explanation.

---

Part F - Fill in the Blanks

1. Mechanical energy is the sum of ______ and ______.
2. Gravity is a ______ force.
3. Potential energy converts into ______ during free fall.
4. Work done in a closed path is ______.
5. Mechanical energy remains ______ when only conservative forces act.

Answers:

1. Kinetic energy, Potential energy
2. Conservative
3. Kinetic energy
4. Zero
5. Constant

---

Part G - Match the Columns

Column A	Column B
Gravity	Conservative force
Friction	Non-conservative force
Potential Energy	mgh
Kinetic Energy	½mv²

Matching Answers 1 → Conservative force 2 → Non-conservative force 3 → mgh 4 → ½mv²

---

Part H - Case Study

A ball of mass 2 kg is dropped from a height of 20 m. Ignore air resistance.

Q1. Which energy is maximum at the top?

Answer: Potential Energy

Q2. Which energy is maximum at the ground?

Answer: Kinetic Energy

Q3. Calculate total mechanical energy at the top. Take g = 10 m/s².

PE = mgh = 2 × 10 × 20 = 400 J Answer = 400 Joule

Q4. Is mechanical energy conserved?

Yes. Only gravity acts.

---

Important Formulae

• E = KE + PE
• KE = ½mv²
• PE = mgh
• Ki + Ui = Kf + Uf
• Δ(KE + PE) = 0
• v = √(2gH)
• v² = 2g(H − h)
• Work in closed path = 0

---

End of CBSE Class 11 Physics Question Bank

Standard of Comparison (Large and Small Physical Quantities)

 Standard of Comparison Explained | CBSE Class 11 Physics | NEET Notes 

Standard of Comparison in Physics with real-life examples for NEET and CBSE students.

- Dr. Sanjaykumar Pawar 

Q. 1.4 Explain this statement clearly:

“To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison.”

Answer (CBSE Topper Style)

A dimensional physical quantity has both magnitude and unit. Whether it is called large or small depends on what it is being compared with.

Therefore, simply saying that a quantity is "large" or "small" has no meaning unless a standard or reference quantity is mentioned.

Example:

• A distance of 10 m is large compared to the size of a classroom but very small compared to the distance between two cities.

Hence, every statement describing a dimensional quantity as large or small should include a suitable standard of comparison.

---

Reframing the given statements

(a) Atoms are very small objects.

Reframed Statement:
Atoms are very small compared to ordinary objects, such as a grain of sand or a pinhead.

---

(b) A jet plane moves with great speed.

Reframed Statement:
A jet plane moves with great speed compared to road vehicles, but its speed is much smaller than the speed of light.

---

(c) The mass of Jupiter is very large.

Reframed Statement:
The mass of Jupiter is very large compared to the mass of the Earth (or any other planet like Mars).

---

(d) The air inside this room contains a large number of molecules.

Reframed Statement:
The air inside this room contains a very large number of molecules compared to the number of people or other visible objects present in the room.

---

(e) A proton is much more massive than an electron.

Answer:
This statement is already meaningful because it clearly specifies the standard of comparison (electron).

---

(f) The speed of sound is much smaller than the speed of light.

Answer:
This statement is already meaningful because it compares the speed of sound with the speed of light, providing a clear standard of comparison.

---

Final Answer (Exam Points)

• A quantity can be called large or small only with respect to a specified standard or reference.
• Without comparison, such statements are meaningless.

Corrected Statements:

(a) Atoms are very small compared to ordinary objects.
(b) A jet plane moves with great speed compared to road vehicles.
(c) The mass of Jupiter is very large compared to the mass of the Earth.
(d) The air inside this room contains a very large number of molecules compared to the number of people in the room.
(e) No change required, as the comparison is with an electron.
(f) No change required, as the comparison is with the speed of light. 

NEET Master Learning Structure (NMLS)

हर टॉपिक के लिए एक यूनिवर्सल फॉर्मेट

---

1. Topic Name

Chapter: Units and Measurements

Topic: Standard of Comparison (Large & Small Quantities)

---

2. One-Line Definition (Exam Definition)

Rule:

किसी भी भौतिक राशि (Physical Quantity) को "बड़ा" या "छोटा" तभी कहा जा सकता है जब उसके साथ तुलना (Comparison) का मानक (Standard) दिया गया हो।

---

3. Why? (Concept Building)

याद रखने वाला नियम

👉 बड़ा या छोटा = हमेशा तुलना

यदि तुलना नहीं है तो कथन अधूरा है।

---

4. Visual Flow Chart

Physical Quantity
        │
        ▼
Large / Small ?
        │
        ▼
Compared With?
      /      \
    Yes      No
    │         │
Meaningful  Meaningless

---

5. Memory Trick (Mnemonic)

Mnemonic

"LSC"

L → Large

S → Small

C → Comparison

Large or Small ⇒ Comparison Must

---

दूसरा आसान Mnemonic

"No Comparison = No Conclusion"

(NC = NC)

---

6. Quick Table

Statement	Comparison Given?	Correct / Incorrect
Atom is small	❌ No	Incorrect
Atom is smaller than a grain of sand	✅ Yes	Correct
Jet is fast	❌ No	Incorrect
Jet is faster than a car	✅ Yes	Correct
Proton is heavier than electron	✅ Yes	Correct
Speed of sound is less than speed of light	✅ Yes	Correct

---

7. Comparison Table

Quantity	Compared With	Final Statement
Atom	Everyday objects	Very small
Jet Plane	Car	Very fast
Jupiter	Earth	Very massive
Air Molecules	Humans	Very large number
Proton	Electron	Much heavier
Sound	Light	Much slower

---

8. Mind Map

             Large / Small
                    │
        ┌───────────┼───────────┐
        │           │           │
     Heavy       Fast       Long
        │           │           │
        └───────────┼───────────┘
                    │
          Need Comparison
                    │
           Otherwise Wrong

---

9. Common Mistakes

❌ Atom is very small.

✔ Atom is very small compared to everyday objects.

---

❌ Car is very fast.

✔ Car is faster than a bicycle.

---

❌ Jupiter is very massive.

✔ Jupiter is much more massive than Earth.

---

10. Examiner's Favourite Questions

Type-1

Explain why comparison is necessary.

---

Type-2

Rewrite the statement correctly.

---

Type-3

Which statement is meaningful?

---

Type-4

Assertion-Reason

---

Type-5

Choose the incorrect statement.

---

11. NEET Trick

Whenever you read these words

Large

Small

Heavy

Light

Fast

Slow

High

Low

Long

Short

Immediately ask

"Compared to What?"

यदि उत्तर मिल गया

✅ Statement Correct

यदि उत्तर नहीं मिला

❌ Statement Incorrect

---

12. PYQ Thinking Method

Question पढ़ते ही

STEP-1

Physical Quantity पहचानो

↓

STEP-2

Large/Small लिखा है?

↓

STEP-3

Comparison दिया है?

↓

Yes → Correct Statement

No → Wrong Statement

---

13. 10-Second Revision

✔ Large = Relative

✔ Small = Relative

✔ Heavy = Relative

✔ Fast = Relative

✔ Comparison Must

✔ No Comparison = No Meaning

---

14. Golden Rule (100% Exam Point)

यदि किसी वाक्य में Large, Small, Heavy, Light, Fast, Slow, High या Low लिखा हो, तो तुरंत जाँचें कि तुलना (Comparison) दी गई है या नहीं।

यदि तुलना नहीं दी गई है, तो कथन वैज्ञानिक रूप से अधूरा (Meaningless) माना जाएगा।

---

15. One-Line Formula

Large/Small + Comparison = Meaningful Statement

Large/Small − Comparison = Meaningless Statement

NEET Practice Question Bank

Chapter: Units and Measurements

Topic: Standard of Comparison (Large & Small Quantities)

---

Section A: Direct MCQs (Single Correct Option)

Easy Level

Q1.

Which of the following statements is scientifically meaningful?

A. A mountain is very high.

B. An atom is very small.

C. A proton is more massive than an electron.

D. A river is very long.

✅ Answer: C

Explanation: Only option C provides a standard of comparison.

---

Q2.

Which statement is incomplete?

A. Earth is larger than the Moon.

B. Light travels faster than sound.

C. Jupiter is more massive than Earth.

D. A train is very fast.

✅ Answer: D

---

Moderate Level

Q3.

Which statement correctly follows the principle of comparison?

A. Molecules are tiny.

B. A jet plane is fast compared to a bicycle.

C. A room contains many molecules.

D. The Sun is hot.

✅ Answer: B

---

Q4.

Which statement is NOT meaningful?

A. A proton is heavier than an electron.

B. Sound travels slower than light.

C. Mercury is smaller than Earth.

D. Iron is very heavy.

✅ Answer: D

---

Hard Level

Q5.

Which option correctly identifies all meaningful statements?

1. Atom is very small.

2. Proton is heavier than electron.

3. Speed of light is greater than speed of sound.

4. Jupiter is very massive.

Options

A. 1 and 4

B. 2 and 3

C. 1,2,3

D. All

✅ Answer: B

---

Section B: Statement-Based Questions

Q6.

Statement I

Every physical quantity described as "large" or "small" requires a comparison.

Statement II

Without a standard of comparison, such statements are scientifically incomplete.

A. Both statements are true and II explains I.

B. Both true but II does not explain I.

C. I true II false.

D. I false II true.

✅ Answer: A

---

Q7.

Statement I

The statement "An atom is very small" is scientifically complete.

Statement II

A meaningful statement must include a standard of comparison.

A. TT

B. TF

C. FT

D. FF

✅ Answer: C

---

Section C: Assertion & Reason

Q8.

Assertion (A)

"The speed of sound is much smaller than the speed of light."

Reason (R)

The statement specifies a standard for comparison.

A. Both A and R are true, and R is the correct explanation.

B. Both true but R is not the explanation.

C. A true R false.

D. A false R true.

✅ Answer: A

---

Q9.

Assertion

"A jet plane moves with great speed."

Reason

The statement gives the comparison standard.

A. TT Correct Explanation

B. TT Wrong Explanation

C. TF

D. FT

✅ Answer: C

---

Section D: Match the Columns

Column I

A. Atom

B. Proton

C. Sound

D. Jupiter

Column II

1. Compared with Earth

2. Compared with Electron

3. Compared with Light

4. Compared with Everyday Objects

Correct Matching

A → 4

B → 2

C → 3

D → 1

Answer

A-4

B-2

C-3

D-1

---

Section E: Diagram-Based Question

Flow Chart

          Statement
               │
               ▼
      Large / Small ?
               │
        ┌──────┴──────┐
        │             │
Comparison Given?   No Comparison
        │             │
        ▼             ▼
Meaningful      Meaningless

Question

The statement

"Gold is heavy."

lies in which branch?

A. Meaningful

B. Meaningless

C. Dimensionless

D. Scalar

✅ Answer: B

---

Section F: Higher Order Thinking (HOTS)

Q10.

A student writes

"The Earth is very large."

The teacher marks it incorrect.

Which correction is most appropriate?

A. Earth is large compared to the Moon.

B. Earth is always large.

C. Earth is absolutely large.

D. Earth has a large radius.

✅ Answer: A

---

Q11.

Which one of the following is an example of a relative statement?

A. Length is measured in metre.

B. Speed of light is constant.

C. The Himalayas are higher than the Aravalli Hills.

D. Mass is a fundamental quantity.

✅ Answer: C

---

Section G: NEET PYQ-Type Mixed MCQs

Q12.

Identify the meaningful statements.

1. Air contains many molecules.

2. Jupiter is more massive than Earth.

3. Electron is lighter than proton.

4. Mountain is very high.

Options

A. 1,2

B. 2,3

C. 1,3

D. All

✅ Answer: B

---

Q13.

Which of the following words usually require a comparison to become scientifically meaningful?

1. Large

2. Small

3. Fast

4. Heavy

Options

A. Only 1

B. 1 and 2

C. 1,2,3

D. All

✅ Answer: D

---

Section H: Very Hard NEET Conceptual Question

Q14.

Which statement best explains why "The Sun is very large" is scientifically incomplete?

A. The Sun is not large.

B. Size has no unit.

C. No comparison standard has been specified.

D. The Sun's mass is unknown.

✅ Answer: C

---

Section I: NEET Trap Question

Q15.

Which one is correctly written?

A. Atom is tiny.

B. Jupiter is huge.

C. Proton is much heavier than electron.

D. Car is fast.

✅ Answer: C

---

Final Revision Trick

Whenever you read these words in a NEET question:

✔ Large

✔ Small

✔ Heavy

✔ Light

✔ Fast

✔ Slow

✔ High

✔ Low

Immediately ask:

👉 "Compared to What?"

If comparison is given → Correct

If comparison is missing → Incorrect or Incomplete

 Internal Links

From this article link to

✔ Physical Quantities

✔ Fundamental and Derived Quantities

✔ SI Units

✔ International System of Units

✔ Dimensions

✔ Dimensional Formula

✔ Dimensional Analysis

✔ Significant Figures

✔ Errors in Measurement

✔ Scientific Notation

✔ Order of Magnitude

✔ Accuracy and Precision

✔ Vernier Calipers

✔ Screw Gauge

✔ NCERT Class 11 Physics Chapter 2 Notes

✔ NEET Physics MCQ Collection

✔ Physics Formula Sheet

✔ Previous Year Questions 

NEET Smart Learning Structure | Mnemonics, Tables & Tricks for Physics & Chemistry

 - Dr.Sanjaykumar Pawar  

Best NEET Study Notes Format with Memory Tricks, Tables & Shortcuts 

Smart NEET Learning Structure with Mnemonics, Formula Tables, and Revision Strategy for Faster Exam Preparation

🔗 INTERNAL LINKING

✔ /neet-study-material

✔ /physics-formulas-class-11

✔ /chemistry-short-notes

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✔ /flashcards-for-neet

✔ /cbse-class-11-science-notes 

✔️/CBSE class 11 physics unit and dimensions NCERT solutions

CBSE Class 9 Science

Fill in the Blanks (Solved Step by Step)

Question:
(a) The volume of a cube of side 1 cm is equal to ______ m³.

Given:
Side = 1 cm = 0.01 m

Volume of Cube = (Side)³

Volume = (0.01)³

= 0.000001 m³

= 1 × 10^-6 m³

Answer: 1 × 10^-6 m³

Question:
(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ______ (mm)².

Given:

• Radius = 2 cm
• Height = 10 cm

Total Surface Area = 2πr(r+h)

= 2 × (22/7) × 2 × (2 + 10)

= 150.86 cm²

1 cm² = 100 mm²

150.86 × 100

= 15086 mm²

Answer: 15086 mm²

Question:
(c) A vehicle moving with a speed of 18 km h^-1 covers ______ m in 1 s.

Convert speed into m/s.

18 × 5/18 = 5 m/s

Distance = Speed × Time

= 5 × 1

= 5 m

Answer: 5 m

Question:
(d) The relative density of lead is 11.3. Its density is ______ g cm^-3 or ______ kg m^-3.

Relative Density = 11.3

Density of Water = 1 g/cm³

Density of Lead

= 11.3 × 1

= 11.3 g/cm³

1 g/cm³ = 1000 kg/m³

11.3 × 1000

= 11300 kg/m³

Answer: 11.3 g/cm³ or 11300 kg/m³

Short Notes

1. Volume of a Cube

• Volume is the space occupied by a body.
• Formula: Volume = Side³
• SI Unit = m³
• 1 cm³ = 10^-6 m³

2. Surface Area of a Cylinder

• Total Surface Area = 2πr(r+h)
• SI Unit = m²
• 1 cm² = 100 mm²

3. Speed and Distance

• Speed = Distance / Time
• Distance = Speed × Time
• 1 km/h = 5/18 m/s

4. Density

• Density = Mass / Volume
• SI Unit = kg/m³
• CGS Unit = g/cm³

5. Relative Density

• Relative Density = Density of Substance / Density of Water
• It has no unit.
• Density (g/cm³) = Relative Density × 1

Important Conversions

• 1 cm = 10^-2 m
• 1 cm³ = 10^-6 m³
• 1 cm² = 100 mm²
• 1 g/cm³ = 1000 kg/m³
• 1 km/h = 5/18 m/s

NEET Practice Questions

Units, Measurements & Density

Q1. The volume of a cube having side 2 cm is
A. 2 × 10⁻⁶ m³
B. 4 × 10⁻⁶ m³
C. 8 × 10⁻⁶ m³
D. 16 × 10⁻⁶ m³

Answer: C

Volume = 2³ = 8 cm³ = 8 × 10⁻⁶ m³

Q2. A vehicle moves with speed 72 km/h. Its speed in m/s is

Answer: C (20 m/s)

72 × 5/18 = 20 m/s

Q3. The SI unit of density is
A. g/cm³
B. kg/m³
C. kg/cm³
D. g/m³

Answer: B

Q4. Relative density has

Answer: C (No unit)

Q5. 1 g/cm³ is equal to
A. 10 kg/m³
B. 100 kg/m³
C. 1000 kg/m³
D. 10000 kg/m³

Answer: C

Q6. Total surface area of a cylinder is
A. 2πrh
B. πr²h
C. 2πr(r+h)
D. π(r+h)

Answer: C

Q7. Density of water is

Answer: B (1 g/cm³)

Q8. Relative density of a substance is 13.6, its density is

Answer: B (13.6 g/cm³)

Q9. Convert 5000 kg/m³ into g/cm³

Answer: B (5 g/cm³)

1000 kg/m³ = 1 g/cm³ → 5000 = 5 g/cm³

Q10. Dimensional formula of density is
A. MLT⁻²
B. ML⁻³
C. MLT
D. ML²

Answer: B

Assertion Reason

Q11. Assertion: Relative density has no unit.
Reason: It is ratio of two densities.

Answer: A

Q12. Assertion: Density depends on mass and volume.
Reason: Density = Mass/Volume

Answer: A

Integer Type

Q13. Cube side = 5 cm, volume?

Answer: 125 cm³

Q14. Convert 36 km/h into m/s

Answer: 10 m/s

Q15. 11300 kg/m³ in g/cm³

Answer: 11.3 g/cm³

Tricky Questions

Q16. Which has no dimensions?

Answer: C (Relative density)

Q17. If cube side is doubled, volume becomes?

Answer: D (8 times)

Q18. If radius and height doubled, TSA becomes?

Answer: B (4 times)

Quick Revision

Density = M/V
Relative density = No unit
1 cm³ = 10⁻⁶ m³
1 g/cm³ = 1000 kg/m³
18 km/h = 5 m/s
Cylinder TSA = 2πr(r+h)

NEET Smart Learning Structure

1. Topic Name

Units and Measurements

2. One-Line Definition

✔ Volume = किसी वस्तु द्वारा घेरा गया स्थान
✔ Density = प्रति इकाई आयतन में द्रव्यमान
✔ Relative Density = पदार्थ की घनत्व / पानी की घनत्व

3. Formula Table

Quantity	Formula	SI Unit	Conversion
Volume	Side³	m³	1 cm³ = 10⁻⁶ m³
Density	Mass/Volume	kg/m³	1 g/cm³ = 1000 kg/m³
Speed	Distance/Time	m/s	1 km/h = 5/18 m/s
Cylinder TSA	2πr(r+h)	m²	1 cm² = 100 mm²

4. Memory Table

1 cm = 10⁻² m → Centi = -2
1 cm² = 100 mm² → Square rule
1 cm³ = 10⁻⁶ m³ → Cube rule
1 g/cm³ = 1000 kg/m³ → Thousand rule
18 km/h = 5 m/s → Shortcut trick

5. Mnemonics

Density: M/V (Mass over Volume)

Speed Triangle:
D
---
S T

Cube Conversion: 2-4-6 Rule

6. NEET Trap Points

❌ Relative Density has no unit
❌ Area → square conversion always
❌ Volume → cube conversion always
❌ 18 km/h = 5 m/s important trick

7. Exam Strategy Flow

Unit → Formula → Conversion → Calculation → Option Match

8. Flash Cards

Q: Density Formula?
A: Mass/Volume

Q: Relative Density Unit?
A: No Unit

Q: 1 cm³?
A: 10⁻⁶ m³

Q: 18 km/h?
A: 5 m/s

9. Mind Map

Units
├── Length
├── Area
├── Volume
├── Density
├── Relative Density
├── Speed
└── Conversion

↓
Formulas
↓
Memory Tricks
↓
PYQs
↓
NEET Ready

CBSE Class 11 Physics: Point Object MCQ with Topper Answer

 When Can a Body Be Considered a Point Object? CBSE Class 11 Solution

Q1. In which of the following examples of motion can the body be considered approximately a point object? 

Examples showing when a body can and cannot be considered a point object in Class 11 Physics.

 

- Dr. Sanjay Kumar Pawar 

Principle: A body can be considered a point object if the distance travelled by it is much greater than its own size (dimensions).

(a) A railway carriage moving without jerks between two stations.

Answer: Yes, the railway carriage can be considered a point object.

Explanation: The distance between two stations is very large compared to the length of the carriage. Hence, the size of the carriage is negligible in comparison to the distance travelled. Therefore, it can be treated as a point object.

(b) A cap on top of a man cycling smoothly on a circular track.

Answer: Yes, the cap can be considered a point object.

Explanation: The size of the cap is very small compared to the circumference of the circular track covered during motion. Therefore, its dimensions can be neglected and it may be treated as a point object.

(c) A spinning cricket ball that turns sharply on hitting the ground.

Answer: No, the cricket ball cannot be considered a point object.

Explanation: The sharp turn of the spinning ball involves rotational motion, and the distance over which the change in direction occurs is comparable to the size of the ball. Hence, its dimensions cannot be neglected.

(d) A tumbling beaker that has slipped off the edge of a table.

Answer: No, the beaker cannot be considered a point object.

Explanation: The size of the beaker is comparable to the height through which it falls. Moreover, tumbling involves rotational motion. Therefore, the dimensions of the beaker are important and it cannot be treated as a point object.

Conclusion

Hence, the body can be considered approximately a point object in cases (a) and (b) only.

Final Answer: (a) and (b)

Topper's Tip for the Exam:

​The Core Principle: Always state the rule first. An object can be considered a point object if the distance it travels during its motion is much greater than its own linear dimensions.

बहुत अच्छा विचार है। NEET/CBSE Physics के किसी भी टॉपिक को याद करने और ट्रिकी प्रश्न हल करने के लिए "4-Layer Topper Memory Structure" सबसे प्रभावी रहता है। आपके दिए हुए "Point Object" वाले प्रश्न को उदाहरण बनाकर यह संरचना तैयार की जा सकती है।

NEET में इस प्रकार उत्तर Explain करें:

1. पहले Rule लिखें।
2. फिर Distance vs Size की तुलना करें।
3. अंत में Yes/No लिखें।
4. यदि rotation या tumbling हो तो उल्लेख करें कि आकार और orientation महत्वपूर्ण हो जाते हैं।

Practice Questions: Point Object (CBSE Class 11 Physics)

Key Rule

A body can be considered a point object if the distance travelled by it is much greater than its size.

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Question 1

Can an airplane flying from Delhi to Mumbai be considered a point object?

Answer

Yes.

The distance between Delhi and Mumbai is much greater than the size of the airplane. Therefore, the airplane can be treated as a point object while studying its motion.

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Question 2

Can a football rolling across a playground be considered a point object?

Answer

Yes.

The distance covered by the football across the playground is much larger than its diameter. Hence, it can be considered a point object.

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Question 3

Can a spinning top rotating at one place be considered a point object?

Answer

No.

The top is mainly rotating about its own axis. Its size and rotational motion are important. Therefore, it cannot be treated as a point object.

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Question 4

Can a student walking around a 400 m circular track be considered a point object?

Answer

Yes.

The size of the student is very small compared to the distance covered on the track. Hence, the student can be considered a point object.

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Question 5

Can a coin spinning on a table be considered a point object?

Answer

No.

The motion depends on the coin's size and rotation. Therefore, it cannot be treated as a point object.

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Multiple Choice Questions (MCQs)

Question 6

Which of the following can be treated as a point object?

(a) A train travelling between two cities

(b) A rotating ceiling fan

(c) A spinning coin

(d) A tumbling box

Answer

(a) A train travelling between two cities

Reason: Distance travelled is much greater than the train's size.

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Question 7

A body can be treated as a point object when:

(a) Its mass is very small

(b) Its shape is circular

(c) Its size is negligible compared to the distance travelled

(d) It is at rest

Answer

(c) Its size is negligible compared to the distance travelled

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Question 8

A cricket ball moving from one boundary to another on a cricket field can be treated as:

(a) A point object

(b) A rigid body only

(c) A fluid

(d) None of these

Answer

(a) A point object

Reason: The distance covered is much larger than the size of the ball.

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Assertion-Reason Questions

Question 9

Assertion (A): A train moving between two stations can be treated as a point object.

Reason (R): The distance travelled is much greater than the size of the train.

Answer

Both A and R are true, and R is the correct explanation of A.

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Question 10

Assertion (A): A spinning beaker falling from a table can be treated as a point object.

Reason (R): The size of the beaker is important in describing its motion.

Answer

Assertion is false, but Reason is true.

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Exam Tip

Remember:

Distance ≫ Size → Point Object ✅

Distance ≈ Size → Not a Point Object ❌

Easy Trick:

"Long Journey = Point Object"

"Rotation Important = Not Point Object"

Internal Links

What Is Motion in Physics? Class 11 Notes

Difference Between Distance and Displacement

Scalars and Vectors Explained for Class 11

NCERT Solutions for Motion in a Straight Line

Rest and Motion: Important Concepts

Average Speed and Velocity Numericals

Class 11 Physics Chapter-wise NCERT Solutions

Physical Quantities and Units Explained

Relative Motion Basics for Students

Important CBSE Class 11 Physics Questions