Force and Motion — Exercise Solutions
Comprehensive solutions for TN State Board Class 7 Science Term 1 Chapter 2: Force and Motion. Covers MCQs, fill in the blanks, match the following, analogy, very short answers, short answers, detailed answers, and numerical problems.
I. Choose the Appropriate Answer (MCQ)
Q1. A particle is moving in a circular path of radius r. The displacement after half a circle would be:
(a) Zero (b) r (c) 2r ✓ (d) r/2
Q2. From the given v-t graph it can be inferred that the object is:
(a) in uniform motion (b) at rest (c) in non-uniform motion (d) moving with uniform acceleration ✓
Q3. Which of the following figures represents uniform motion of a moving object correctly?
Q4. A boy is enjoying a ride on a merry-go-round moving with constant speed of 10 m/s. It implies that the boy is:
(a) at rest (b) moving with no acceleration (c) in accelerated motion ✓ (d) moving with uniform velocity
Q5. What is one way you might increase the stability of an object?
(a) lower the centre of gravity ✓ (b) raise the centre of gravity (c) increase the height of the object (d) shorten the base
Additional MCQs
Q6 (Additional). Distance travelled by a body in a given time:
(a) is always positive (b) can be zero or positive ✓ (c) is always negative (d) either (a) or (c)
Q7 (Additional). Which of the following is correct?
(a) magnitude of displacement may be greater than distance (b) Distance is always greater than or equal to the magnitude of displacement ✓ (c) Distance is always greater than the magnitude of displacement (d) Both are scalar quantities
Q8 (Additional). Average speed equals magnitude of average velocity when the object travels:
(a) in a straight line without turning back ✓ (b) in a circle (c) back and forth (d) in a zig-zag path
Q9 (Additional). The slope of a velocity-time graph gives:
(a) velocity (b) distance (c) displacement (d) acceleration ✓
Q10 (Additional). Velocity-time graph of an object shows a straight line sloping downward. The object has:
(a) uniform velocity (b) uniform retardation ✓ (c) uniform speed (d) variable retardation
Q11 (Additional). If the velocity of a body does not change, then its acceleration is:
(a) Infinity (b) unity (c) Zero ✓ (d) between zero and unity
II. Fill in the Blanks
1. The shortest distance between two places is displacement. 2. The rate of change of velocity is acceleration. 3. If the velocity of an object increases with respect to time, then the object is said to be in positive acceleration. 4. The slope of the speed-time graph gives velocity. 5. In neutral equilibrium, its centre of gravity remains at the same height when it is displaced.
Additional Fill in the Blanks
6. The SI unit of displacement is metre (m). 7. The SI unit of speed is m/s. 8. Distance is the length of actual path covered by a body. 9. Speed is the distance travelled by a body per unit time. 10. Distance is a scalar quantity. 11. The displacement is zero when the initial and final positions are same. 12. Speed is always positive or zero but never negative. 13. When the velocity of a body increases with time, its acceleration is positive. 14. The acceleration of a body moving with uniform velocity is zero. 15. A car increases speed from 20 km/h to 50 km/h in 10 s. Its acceleration is 0.83 m/s².
III. Match the Following
Set 1 (Textual):
| Column I | Column II | Answer |
|---|---|---|
| 1. Displacement | (a) Knot | (c) Metre |
| 2. Light travels through vacuum | (b) Geometric centre | (e) Uniform velocity |
| 3. Speed of ship | (c) Metre | (a) Knot |
| 4. Centre of gravity of geometrical shaped object | (d) Larger base area | (b) Geometric centre |
| 5. Stability | (e) Uniform velocity | (d) Larger base area |
Set 2 (Additional):
| Column I | Column II | Answer |
|---|---|---|
| a. Uniform motion | (i) Body having uniform acceleration | (iv) Equal distances covered in equal intervals of time |
| b. Non-uniform motion | (ii) Body at rest | (iii) Unequal distances covered in equal intervals of time |
| c. Velocity-time graph is a circle | (iii) Unequal distances covered in equal intervals of time | (v) Not possible |
| d. Straight line parallel to time axis in position-time graph | (iv) Equal distances covered in equal intervals of time | (i) Body having uniform acceleration |
| e. Straight line inclined to 45° with time axis in velocity-time graph | (v) Not possible | (ii) Body at rest |
IV. Analogy
Q1. velocity : metre/second :: acceleration : metre/second²
Q2. length of scale : metre :: speed of aeroplane : knot
Q3. displacement/time : velocity :: speed/time : acceleration
V. Very Short Answer Questions
Q1. All objects having uniform speed need not have uniform velocity. Describe with examples.
An object moving in uniform circular motion has constant speed but changing velocity because direction keeps changing. Examples: merry-go-round, roller coaster car, planets orbiting the Sun.
Q2. "She moves at a constant speed in a constant direction." Rephrase in fewer words.
She moves in a straight line with constant velocity.
Q3. Correct your friend who says "The acceleration gives the idea of how fast the position changes."
Velocity gives an idea of how fast position changes. Acceleration gives an idea of how fast velocity changes.
Q4 (Additional). Give one example where displacement is zero but distance is not zero.
When an object completes one full circle, displacement is zero (initial and final positions are the same) but distance equals the circumference.
Q5 (Additional). Is displacement a scalar quantity?
No, displacement is a vector quantity because it depends on direction.
Q6 (Additional). Give examples of vector quantities.
Displacement, velocity, force, acceleration, momentum.
Q7 (Additional). Give examples of scalar quantities.
Mass, distance, speed, temperature, time.
Q8 (Additional). Give one example of uniform acceleration.
Motion of a freely falling body under gravity.
Q9 (Additional). Give one example of non-uniform acceleration.
Motion of a car on a crowded road (speed changes erratically).
Q10 (Additional). Give an example of retardation/deceleration.
When a person applies brakes on a moving car, its velocity decreases with time.
Q11 (Additional). What are the three types of stability?
(1) Stable equilibrium (2) Unstable equilibrium (3) Neutral equilibrium
Q12 (Additional). Mention any two conditions for stability of a body.
(1) Increase the area of its base (2) Lower its centre of gravity.
VI. Short Answer Questions
Q1. Show the shape of the distance-time graph for: (a) A bus moving with constant speed (b) A car parked on a roadside.
(a) A straight line inclined to the time axis, starting from the origin. (b) A horizontal line parallel to the time axis (position remains constant, distance does not change).
Q2. Distinguish between speed and velocity.
| Speed | Velocity |
|---|---|
| Rate of change of distance | Rate of change of displacement |
| Scalar quantity (magnitude only) | Vector quantity (magnitude + direction) |
| Always positive or zero | Can be positive, negative, or zero |
| Depends only on magnitude | Depends on both magnitude and direction |
Q3. What is constant acceleration?
A body has constant acceleration if it travels in a straight line and its velocity increases or decreases by equal magnitude in equal intervals of time. Example: motion of a freely falling body under gravity (acceleration = 9.8 m/s²).
Q4. What is centre of gravity?
The centre of gravity of an object is the point through which the entire weight of the object appears to act. For regularly shaped objects, it is at their geometric centre.
Q5 (Additional). A body moves in a circle of radius 2R. What is the distance covered and displacement after 2 complete rounds?
- Distance = 2 × circumference = 2 × 2π(2R) = 8πR
- Displacement = 0 (the body returns to its starting position after 2 complete rounds)
Q6 (Additional). What are the uses of graphical study of motion?
(1) By looking at the graph, one can tell whether motion is uniform or not. (2) It is useful for comparing the motions of two or more moving bodies.
Q7 (Additional). Draw distance-time graphs for: (1) a stationary body (2) a body moving with variable velocity.
(1) A horizontal line parallel to the time axis (distance constant). (2) A curved line showing varying slope (speed changes over time).
Q8 (Additional). Mention real-life applications of centre of gravity.
(1) Luggage compartment of a tour bus is located at the bottom, not on the roof — lowers centre of gravity. (2) Racing cars are built low and broad for stability. (3) Table lamps and fans have large heavy bases for stability.
Q9 (Additional). Explain the concept used in the continuous movement of the Thanjavur doll.
The centre of gravity and total weight of the Thanjavur doll is concentrated at its bottom-most point. This generates a dance-like continuous movement with slow oscillations, making it a popular traditional toy.
Q10 (Additional). Write notes on: (1) Nautical mile (2) Knot.
(1) Nautical mile is the unit for measuring distance in aviation and sea transportation. One nautical mile = 1.852 km. (2) Knot is the unit for measuring speed of aeroplanes and ships. One knot = speed to travel one nautical mile per hour.
Q11 (Additional). Define speed with formula and unit.
Speed is the rate of change of distance. Formula: Speed = Distance / Time. SI unit: m/s.
Q12 (Additional). Define velocity with formula and unit.
Velocity is the rate of change of displacement. Formula: Velocity = Displacement / Time. SI unit: m/s (direction must be specified).
Q13 (Additional). What is uniform velocity? Give one example.
A body has uniform velocity if it covers equal displacement in the same direction in equal intervals of time. Example: light travelling through vacuum.
Q14 (Additional). What is non-uniform velocity? Give an example.
If either speed or direction changes, the velocity is non-uniform. Example: a train starting from rest and accelerating out of a station.
Q15 (Additional). Define acceleration with formula and unit.
Acceleration is the rate of change in velocity. Formula: a = (v − u) / t, where v = final velocity, u = initial velocity, t = time. SI unit: m/s².
Q16 (Additional). Define positive acceleration and negative acceleration.
(i) Positive acceleration: When velocity of an object increases with time. Example: a car speeding up. (ii) Negative acceleration (retardation/ deceleration): When velocity of an object decreases with time. Example: a car braking to a stop.
VII. Detailed Answer Questions
Q1. Explain the types of stability with suitable examples.
Stability is a measure of a body's ability to maintain its original position. Three types:
1. Stable Equilibrium: The object can be tilted through a large angle without toppling. Its centre of gravity is raised when displaced, and the vertical line through its centre of gravity still falls within its base, so it returns to its original position. Example: a frustum placed on its larger base.
2. Unstable Equilibrium: The object topples with the slightest tilting. Its centre of gravity is lowered when displaced, and the vertical line through its centre of gravity falls outside its base. Example: a frustum placed on its smaller base.
3. Neutral Equilibrium: The object rolls but does not topple. Its centre of gravity remains at the same height when displaced, and it stays in any position to which it has been displaced. Example: a sphere or cylinder rolling on a flat surface.
Q2. Describe the experiment to find the centre of gravity of an irregularly shaped plate.
1. Make three small holes at different points on the lamina (irregular plate). 2. Suspend the lamina from an optical pin through one of the holes. 3. Suspend a plumb line from the same pin and mark its position on the lamina. 4. Draw a line on the lamina representing the position of the plumb line. 5. Repeat the above steps for the other two holes. 6. The intersection of the three lines is marked as X — this is the centre of gravity of the lamina.
Q3. Write the differences between distance and displacement.
| Distance | Displacement |
|---|---|
| Total length of path taken by an object between two places | Shortest distance from initial to final position |
| May be different for different paths chosen | Always the same between two given points |
| Scalar quantity (magnitude only) | Vector quantity (magnitude + direction) |
| Always positive or zero | May be positive, negative, or zero |
| Depends on the path taken | Does not depend on the path taken |
VIII. Numerical Problems
Q1. Geetha takes 15 minutes from her house to reach school on a bicycle at speed 2 m/s. Calculate the distance.
- Time = 15 min = 15 × 60 = 900 s; Speed = 2 m/s
- Distance = Speed × Time = 2 × 900 = 1,800 m
Q2. A car started from rest and reaches 20 m/s in 10 s. Find its acceleration.
- u = 0, v = 20 m/s, t = 10 s
- a = (v − u) / t = (20 − 0) / 10 = 2 m/s²
Q3. A bus accelerates at 1 m/s². Find the minimum time to reach 100 km/s from 50 km/s.
- a = 1 m/s²; u = 50 × 10³ m/s; v = 100 × 10³ m/s
- t = (v − u) / a = (100,000 − 50,000) / 1 = 50,000 s
Q4 (Additional). Saranya jogs from end A to end B of a straight 320 m road in 2 min 40 s, then turns back and jogs 100 m to point C in 1 min. Find average velocity.
- Displacement from A to C = 320 − 100 = 220 m
- Total time = 3 min 40 s = 220 s
- Average velocity = 220 / 220 = 1 m/s
Q5 (Additional). A train starting from rest attains 40 km/h in 10 minutes. Find acceleration.
- u = 0; v = 40 km/h; t = 10/60 h = 1/6 h
- a = (40 − 0) / (1/6) = 40 × 6 = 240 km/h²
IX. Distance and Displacement Table
| First Move | Second Move | Distance | Displacement |
|---|---|---|---|
| 4 m east | 2 m west | 6 m | 2 m east |
| 4 m north | 2 m south | 6 m | 2 m north |
| 2 m east | 4 m west | 6 m | 2 m west |
| 5 m east | 5 m west | 10 m | 0 (same place) |
| 5 m south | 2 m north | 7 m | 3 m south |
| 10 m west | 3 m east | 13 m | 7 m west |
Common Mistakes to Avoid
1. Confusing distance and displacement — Distance is scalar (path length); displacement is vector (shortest path with direction). They are equal only in straight-line motion without turning back. 2. Saying force is needed to keep an object moving at constant speed — Newton's first law states that an object continues in uniform motion unless acted upon by an external force. 3. Confusing speed and velocity — Speed is scalar (magnitude only); velocity is vector (magnitude + direction). Constant speed does not mean constant velocity in circular motion. 4. Forgetting direction in displacement — Displacement must include direction (east, north, etc.). Without direction, it is not a complete answer. 5. Assuming zero speed means zero velocity and vice versa — Zero speed means zero velocity, but zero velocity can also occur when an object reverses direction (instantaneous zero). 6. Mixing up positive and negative acceleration — When velocity increases, acceleration is positive; when velocity decreases, acceleration is negative (retardation). 7. Confusing centre of gravity with geometric centre — They coincide only for uniform, regularly shaped objects. For irregular objects, the centre of gravity must be found experimentally.
Exam Checklist
- [ ] Can define and distinguish distance, displacement, speed, and velocity
- [ ] Can explain the three types of stability with examples
- [ ] Can describe the experiment to find centre of gravity of an irregular lamina
- [ ] Can interpret distance-time and velocity-time graphs
- [ ] Can solve numerical problems using v = u + at, s = ut + ½at², and a = (v−u)/t
- [ ] Can give examples of scalar and vector quantities
- [ ] Can explain uniform and non-uniform acceleration with examples
- [ ] Know the relationship between slope of graphs and physical quantities
- [ ] Can distinguish between distance-time and velocity-time graphs
- [ ] Can explain why circular motion involves acceleration even at constant speed