CBSE Class 11 Physics (Motion Under Free Fall) – Question Bank with Answers
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| Motion of an object under free fall showing acceleration, velocity, and displacement-time graphs. |
A. Multiple Choice Questions (MCQs)
1. A body is said to be in free fall when:
a) It falls with constant velocity
b) It falls under gravity only
c) It falls in vacuum only
d) It moves downward
Answer: b) It falls under gravity only
2. The acceleration due to gravity near Earth's surface is:
a) 8.9 m/s²
b) 9.8 m/s²
c) 10.8 m/s²
d) 12 m/s²
Answer: b) 9.8 m/s²
3. The velocity-time graph for a freely falling body is:
a) Horizontal line
b) Parabola
c) Straight line
d) Circle
Answer: c) Straight line
4. The slope of a velocity-time graph represents:
a) Velocity
b) Distance
c) Acceleration
d) Momentum
Answer: c) Acceleration
5. Distance travelled in successive equal intervals of time during free fall follows:
a) 1 : 2 : 3 : 4
b) 2 : 4 : 6 : 8
c) 1 : 3 : 5 : 7
d) 1 : 4 : 9 : 16
Answer: c) 1 : 3 : 5 : 7
6. Stopping distance of a vehicle is proportional to:
a) Speed
b) Square of speed
c) Cube of speed
d) Inverse of speed
Answer: b) Square of speed
7. For a freely falling body released from rest:
a) u = g
b) u = 1
c) u = 0
d) u = 10
Answer: c) u = 0
8. Which equation represents free fall motion?
a) v = u + gt
b) v = u − gt
c) v = u/t
d) v = gt²
Answer: b) v = u − gt
9. The SI unit of acceleration due to gravity is:
a) m
b) m/s
c) m/s²
d) kg
Answer: c) m/s²
10. If speed doubles, stopping distance becomes:
a) Double
b) Triple
c) Four times
d) Eight times
Answer: c) Four times
B. Very Short Answer Questions (1 Mark)
1. Define free fall.
Answer: Motion of a body under the influence of gravity alone is called free fall.
2. What is the value of g near Earth's surface?
Answer: 9.8 m/s².
3. What is the acceleration of a freely falling body?
Answer: g downward.
4. Who proposed the law of odd numbers?
Answer: Galileo Galilei.
5. What is stopping distance?
Answer: Distance travelled by a vehicle after brakes are applied until it comes to rest.
6. What is the slope of a v–t graph?
Answer: Acceleration.
7. What is the shape of displacement-time graph in free fall?
Answer: Parabola.
8. What is the initial velocity of a body released from rest?
Answer: Zero.
C. Short Answer Questions (2–3 Marks)
1. Why is acceleration constant during free fall?
Answer: The only force acting on the body is gravity. Near Earth's surface, gravity remains nearly constant. Therefore acceleration remains constant and equal to g.
2. Write the equations of motion for free fall.
Answer:
3. State Galileo's Law of Odd Numbers.
Answer: The distances covered by a freely falling body during successive equal intervals of time are proportional to odd numbers:
1 : 3 : 5 : 7 : 9 ...
4. Why is the displacement-time graph parabolic?
Answer: Displacement in free fall is proportional to the square of time.
s = \frac{1}{2}gt^2
Since displacement depends on , the graph is a parabola.
5. Explain why stopping distance increases with speed.
Answer: Stopping distance is given by:
d_s = \frac{v_0^2}{2a}
Hence stopping distance is proportional to the square of velocity. Therefore higher speed results in much larger stopping distance.
D. Long Answer Questions (5 Marks)
1. Explain the variation of acceleration, velocity and displacement with time during free fall.
Answer:
(i) Acceleration-Time Graph
- Acceleration remains constant.
- Value = –g.
- Graph is a horizontal straight line.
(ii) Velocity-Time Graph
- Velocity changes uniformly with time.
- Equation:
v = u - gt
- Graph is a straight line with negative slope.
(iii) Displacement-Time Graph
- Displacement increases as square of time.
s = ut - 1/2gt²
- Graph is parabolic.
Thus acceleration is constant, velocity changes uniformly, and displacement changes non-uniformly.
2. Prove Galileo's Law of Odd Numbers.
Answer:
For free fall:
s=1/2gt²
After time t:
s_1=1/2gt²
After 2t:
s_2=4s_1
After 3t:
s_3=9s_1
Distance in successive intervals:
First interval:
s_1
Second interval:
s_2-s_1=3s_1
Third interval:
s_3-s_2=5s_1
Fourth interval:
s_4-s_3=7s_1
Hence ratio:
1:3:5:7
Thus proved.
E. Assertion and Reason Questions
1.
Assertion (A): A freely falling body has constant acceleration.
Reason (R): Gravity acts uniformly near Earth's surface.
Answer: Both A and R are true, and R is the correct explanation of A.
2.
Assertion (A): Stopping distance depends on velocity.
Reason (R): Stopping distance is proportional to velocity squared.
Answer: Both A and R are true, and R is the correct explanation of A.
3.
Assertion (A): Velocity-time graph in free fall is a straight line.
Reason (R): Acceleration remains constant.
Answer: Both A and R are true, and R correctly explains A.
4.
Assertion (A): Displacement-time graph in free fall is linear.
Reason (R): Displacement is proportional to time squared.
Answer: Assertion is false but Reason is true.
F. Fill in the Blanks
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Motion under gravity alone is called free fall.
-
The value of acceleration due to gravity is approximately 9.8 m/s².
-
The slope of a velocity-time graph gives acceleration.
-
Galileo's law follows the ratio 1 : 3 : 5 : 7.
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Stopping distance is proportional to the square of velocity.
-
The SI unit of acceleration is m/s².
-
The displacement-time graph of free fall is a parabola.
-
A body released from rest has initial velocity zero.
G. Case Study Questions
Case Study
A ball is dropped from the top of a tower. It falls freely under gravity. The acceleration remains constant throughout the motion. The velocity increases uniformly while displacement increases rapidly with time.
Questions
1. What is the acceleration acting on the ball?
Answer: g = 9.8 m/s² downward.
2. Which force acts on the ball during free fall?
Answer: Gravitational force.
3. What is the shape of the velocity-time graph?
Answer: Straight line.
4. What is the shape of the displacement-time graph?
Answer: Parabola.
5. Which law explains distances covered in successive seconds?
Answer: Galileo's Law of Odd Numbers.
H. Statement-Based Questions
Statement 1
Acceleration due to gravity remains constant during free fall.
Statement 2
Velocity changes uniformly with time.
a) Both statements are true.
b) Both statements are false.
c) Statement 1 true, Statement 2 false.
d) Statement 1 false, Statement 2 true.
Answer: a) Both statements are true.
Statement 1
Stopping distance is proportional to speed.
Statement 2
Stopping distance is proportional to square of speed.
Answer: Statement 1 is false and Statement 2 is true.
I. Match the Columns
| Column A | Column B |
|---|---|
| 1. Free Fall | a. Gravity only |
| 2. g | b. 9.8 m/s² |
| 3. v–t graph slope | c. Acceleration |
| 4. Galileo | d. Odd number law |
| 5. Stopping Distance | e. Depends on v² |
Answers
1 → a
2 → b
3 → c
4 → d
5 → e
CBSE Exam Important Questions
1. Define free fall and explain its characteristics.
2. Draw and explain acceleration-time, velocity-time and displacement-time graphs for free fall.
3. State and prove Galileo's Law of Odd Numbers.
4. Derive the formula for stopping distance.
5. Explain why stopping distance increases with speed.
6. Write equations of motion for a freely falling body.
7. Differentiate between velocity and acceleration during free fall.
These questions cover MCQs, competency-based questions, assertion-reason, case study, fill in the blanks, statement-based questions, match the columns, short answers, and long answers as per the latest CBSE Class 11 examination pattern.
Internal Links
Motion in a Straight Line Notes
Acceleration and Velocity Concepts
Kinematics Formula Sheet
Free Fall Concepts
Acceleration Due to Gravity Notes
Newton's Law of Universal Gravitation
Projectile Motion Basics
Graph Section
Velocity-Time Graph Explained
Acceleration-Time Graph Problems
Position-Time Graph Interpretation
Galileo Law Section
Motion Under Constant Acceleration
Important NEET Kinematics Questions
NCERT Kinematics Solutions
Stopping Distance Section
Newton's Laws of Motion
Friction Notes Class 11
Braking Force and Retardation Problems
Revision Section
NEET Physics Formula Handbook
Most Important Kinematics Numericals
NEET Physics Previous Year Questions
Motion of an Object Under Free Fall
1. Free Fall – Basic Idea
- When an object falls under the effect of gravity only, the motion is called free fall.
- Air resistance is neglected in free fall problems.
- Acceleration due to gravity is represented by g.
Near Earth’s surface:
- Direction of gravity is always downward.
- If upward direction is taken positive, then acceleration becomes negative.
Fig. 2.7 : Motion of Object Under Free Fall
(a) Variation of Acceleration with Time
- Acceleration remains constant throughout the motion.
- The graph is a horizontal straight line.
- Value of acceleration is always:
Important NEET Point
Constant acceleration means velocity changes uniformly with time.
(b) Variation of Velocity with Time
- Initial velocity for a freely falling body released from rest:
- Velocity increases linearly with time.
- Equation of velocity:
Since (u = 0),
Graph Understanding
- Straight line with negative slope.
- Slope of v–t graph = acceleration = (-g).
Important NEET Concepts
- Velocity becomes more negative with time.
- Body gains speed while falling downward.
(c) Variation of Distance (Position) with Time
- Distance covered in free fall is proportional to square of time.
- Equation of motion:
For (u = 0),
Graph Understanding
- Graph is a parabola.
- Distance increases rapidly with time.
- Motion is non-uniform because velocity changes continuously.
Galileo’s Law of Odd Numbers
Statement
- “The distances travelled during successive equal intervals of time by a freely falling body are in the ratio of odd numbers.”
Ratio is:
Proof in Simple Steps
Step 1: Position after Different Times
For free fall:
After time (t):
After time (2t):
After time (3t):
After time (4t):
Step 2: Distance in Successive Intervals
First Interval
Second Interval
Third Interval
Fourth Interval
Hence ratios become:
Important Result for NEET
For a body starting from rest under gravity:
where:
- (sₙ) = distance travelled in nth second.
Example 2.6 – Stopping Distance of Vehicles
Definition
- Distance travelled by a vehicle before coming to rest after brakes are applied is called stopping distance.
Derivation
Using equation of motion:
For stopping:
- Final velocity (v = 0)
- Initial velocity (u = v₀)
So,
Therefore,
Conclusions
- Stopping distance is proportional to square of initial velocity.
NEET Important Points
- If speed doubles → stopping distance becomes 4 times.
- Stronger brakes mean larger retardation and smaller stopping distance.
Quick Revision Formula Sheet
| Concept | Formula |
|---|---|
| Velocity-Time Relation | v = u - gt |
| Position-Time Relation | s = ut - 1/2 gt² |
| Velocity-Position Relation | v² = u² - 2gs |
One-Line NEET Tricks
- Acceleration due to gravity is constant.
- v–t graph slope gives acceleration.
- Distance in nth second follows odd number rule.
- Stopping distance depends on square of speed.
- Free fall graphs are very important for NEET numericals.
