Lahore board physics

Solved Exercise of Chapter 2 Kinematics: 9th Class Physics

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Get step-by-step solutions for Chapter 2 “Kinematics” from the 9th class physics new syllabus. Specifically designed for Lahore Board and all Punjab Boards, this guide helps students excel in their exams.

MCQs

2.1 The numerical ratio of displacement to distance is:
Options:
(a) always less than one
(b) always equal to one
(c) always greater than one
(d) equal to or less than one

Answer: (d) equal to or less than one
Explanation: Displacement is the shortest distance between two points and can be equal to or less than the actual distance traveled. It cannot exceed the distance.

2.2 If a body does not change its position with respect to some fixed point, then it will be in a state of:
Options:
(a) rest
(b) motion
(c) uniform motion
(d) variable motion

Answer: (a) rest
Explanation: A body is said to be at rest when it does not change its position relative to a reference point.
Tip: Relate to the definition of rest and motion.

2.3 A ball is dropped from the top of a tower; the distance covered by it in the first second is:
Options:
(a) 5 m
(b) 10 m
(c) 50 m
(d) 100 m

Answer: (a) 5 m
Explanation: The distance covered in free fall is given by s=1/2gt2
s=1/2×10×(1)2=5 m
Tip: Memorize the formula s=1/2gt2

2.4 A body accelerates from rest to a velocity of 144 km/h in 20 seconds. Then the distance covered by it is:
Options:
(a) 100 m
(b) 400 m
(c) 1400 m
(d) 1440 m

Answer: (c) 1400 m
Explanation: Convert 144 km/h
v=144×1000/3600=40 m/s
Using the formula s=1/2at2
First, calculate acceleration: a=vt=40/20=2 m/s2
Then, s=1/2×2×202=1400 m
Tip: Convert units before calculations.

2.5 A body is moving with constant acceleration starting from rest. It covers a distance S in 4 seconds. How much time does it take to cover one-fourth of this distance?
Options:
(a) 1 s
(b) 2 s
(c) 4 s
(d) 16 s

Answer: (b) 2 s
Explanation: For constant acceleration, distance is proportional to the square of time:
S∝t2
If the total time is t=4 s, one-fourth of the distance is covered in t/2=2 
Tip: Remember the proportionality S∝t2

2.6 The displacement-time graphs of two objects A and B are shown in the figure. Point out the true statement from the following:
Options:
(a) The velocity of A is greater than B.
(b) The velocity of A is less than B.
(c) The velocity of A is equal to that of B.
(d) The graph gives no information in this regard.

Answer: (a) The velocity of A is greater than B.
Explanation: The slope of a displacement-time graph represents velocity. Since the slope of A’s graph is steeper than B’s, A has a greater velocity.
Tip: Compare slopes for velocity on such graphs.

2.7 The area under the speed-time graph is numerically equal to:
Options:
(a) velocity
(b) uniform velocity
(c) acceleration
(d) distance covered

Answer: (d) distance covered
Explanation: The area under a speed-time graph represents the distance traveled by the object.
Tip: Always associate “area under the curve” with specific physical quantities based on the graph type.

2.8 Gradient of the speed-time graph is equal to:
Options:
(a) speed
(b) velocity
(c) acceleration
(d) distance covered

Answer: (c) acceleration
Explanation: The gradient (slope) of a speed-time graph gives the rate of change of speed, which is acceleration.
Tip: For speed-time graphs:

  • Slope → Acceleration
  • Area under the curve → Distance.

2.9 Gradient of the distance-time graph is equal to:
Options:
(a) speed
(b) velocity
(c) distance covered
(d) acceleration

Answer: (b) velocity
Explanation: The gradient of a distance-time graph represents the rate of change of distance with time, which is velocity.
Tip: Remember, distance-time graph slope indicates motion speed or velocity.

2.10 A car accelerates uniformly from 80.5 km/h at t=0 to 113 km/h at t=9 s. Which graph best describes the motion of the car?
Answer: (a)
Explanation: For uniform acceleration, the velocity-time graph is a straight line with a positive slope, as shown in option (a).
Tip: Uniform acceleration always produces a straight, inclined line in velocity-time graphs.

B: Short Answer Questions

2.1 Define scalar and vector quantities.
Answer:

  • Scalar quantities: Physical quantities that have magnitude only (e.g., mass, temperature).
  • Vector quantities: Physical quantities that have both magnitude and direction (e.g., force, velocity).

2.2 Give 5 examples each for scalar and vector quantities.
Answer:

  • Scalars: Speed, mass, temperature, time, energy.
  • Vectors: Velocity, force, acceleration, displacement, momentum.

2.3 State head-to-tail rule for addition of vectors.
Answer: Place the tail of the second vector at the head of the first vector. The resultant vector is drawn from the tail of the first vector to the head of the second vector.

2.4 What are distance-time graph and speed-time graph?
Answer:

  • Distance-time graph: Represents the motion of an object by plotting distance against time. Slope indicates speed.
  • Speed-time graph: Represents the variation of speed with time. Slope gives acceleration, and the area under the curve gives distance.

2.5 Falling objects near the Earth have the same constant acceleration. Does this imply that a heavier object will fall faster than a lighter object?
Answer: No, all objects fall with the same acceleration (9.8 m/s²) near the Earth, regardless of mass, due to gravity (neglecting air resistance).

2.6 The vector quantities are sometimes written in scalar notation (not bold face). How is the direction indicated?
Answer: Direction is indicated using angles, signs (+/-), or directional symbols (e.g., North, South, East, West).

2.7 A body is moving with uniform speed. Will its velocity be uniform? Give reason.
Answer: Not necessarily. If the body changes direction, the velocity will not remain uniform even if the speed is constant because velocity is a vector quantity (depends on both magnitude and direction).

2.8 Is it possible for a body to have acceleration when moving with:
(i) Constant velocity?
Answer: No, because acceleration is the rate of change of velocity, and with constant velocity, there is no change.
(ii) Constant speed?
Answer: Yes, if the direction changes (e.g., circular motion), there can be centripetal acceleration.

C: Constructed Response Questions

2.1 Distance and displacement may or may not be equal in magnitude. Explain this statement.
Answer:

  • Equal: When the motion is in a straight line without changing direction. For example, walking 5 meters straight.
  • Not Equal: When the motion involves a change in direction, displacement (shortest path) will be less than the distance (total path). For example, walking in a circular path.

2.2 When a bullet is fired, its velocity with which it leaves the barrel is called the muzzle velocity of the gun. The muzzle velocity of one gun with a longer barrel is less than that of another gun with a shorter barrel. In which gun is the acceleration of the bullet larger? Explain your answer.
Answer:
The gun with the shorter barrel has larger acceleration because the same change in velocity (muzzle velocity) occurs over a shorter distance, leading to greater acceleration (since a=v2−u2/2s, where ss is the distance).

2.3 For a car moving at uniform speed, the area under the speed-time graph is calculated. Its value came out to be positive. Is it possible that its instantaneous velocity at any time during the trip had the negative sign? Give justification of your answer.
Answer:
No, because the speed-time graph shows the magnitude of velocity, which is always positive. If the graph is used to compute displacement (not speed), the instantaneous velocity could be negative if the car changes direction.

Comprehensive questions

2.1 How can a vector be represented graphically? Explain.

  • A vector is represented graphically as a directed line segment.
  • The length of the line represents the magnitude of the vector, and the arrowhead shows its direction.
  • For example, if a vector shows a displacement of 5 meters to the right, draw a 5 cm arrow pointing to the right (scale: 1 cm = 1 m).

2.2 Differentiate between:
(i) Rest and Motion:

  • Rest: An object is at rest when it does not change its position relative to a reference point.
    Example: A book lying on a table is at rest.
  • Motion: An object is in motion when it changes its position relative to a reference point.
    Example: A car moving on a road is in motion.

(ii) Speed and Velocity:

  • Speed: It is the rate of change of distance and has no direction (scalar quantity).
    Example: A car moving at 60 km/h.
  • Velocity: It is the rate of change of displacement and includes direction (vector quantity).
    Example: A car moving 60 km/h east.

2.3 Describe different types of motion. Also give examples.

  1. Translational Motion: Movement in a straight or curved path.
    Example: A car driving on a straight road or a ball rolling downhill.
  2. Rotational Motion: Movement around a fixed axis.
    Example: The spinning of a fan.
  3. Oscillatory Motion: Repeated to-and-fro motion.
    Example: The swinging of a pendulum.
  4. Random Motion: Unpredictable movement in any direction.
    Example: The movement of dust particles in the air.

2.4 Explain the difference between distance and displacement.

  • Distance:
    • The total path covered by an object.
    • It is a scalar quantity (only magnitude).
    • Example: If a person walks 4 m north and then 3 m south, the distance is 4+3=7 m
  • Displacement:
    • The shortest straight-line distance between the initial and final position of an object.
    • It is a vector quantity (magnitude and direction).
    • Example: For the same movement above, displacement = 4−3=1 m north.

2.5 What do gradients of distance-time graph and speed-time graph represent? Explain it by drawing diagrams.

  • Distance-Time Graph:
    • The gradient (slope) represents the speed. A steeper slope means higher speed.
    • Example: A straight, slanted line shows uniform speed, while a curved line shows acceleration or deceleration.
  • Speed-Time Graph:
    • The gradient represents acceleration. A straight, inclined line shows uniform acceleration.
    • Example: If the slope is zero (horizontal line), the speed is constant.

2.6 Prove that the area under speed-time graph is equal to the distance covered by an object.

  • The area under a speed-time graph represents the product of speed and time, which gives distance.
  • Proof:
    • Speed = Distance ÷ Time → Distance = Speed × Time
    • For a speed-time graph, the area of a rectangle (or triangle for acceleration) gives the distance:
      • Area = Base × Height = Time × Speed = Distance.
    • Example: For a car moving at 10 m/s for 5 seconds, the graph’s area = 10×5=50 m

2.7 How equations of motion can be applied to bodies moving under the action of gravity?

  • Equations of motion are:
    1. v=u+at
    2. s=ut+1/2at2
    3. v2=u2+2as
  • For objects in free fall:
    • Initial velocity u=0u = 0 (if dropped).
    • Acceleration a=g=9.8 m/s2 (gravity).
  • Example: If a ball is dropped from a height of 20 m:
    • Use s=1/2gt2
      20=1/2(9.8)t2 → t=2.02 s
      The equations help determine time, velocity, or height for objects under gravity.

Chapter 1 Physical Quantities and Measurements Solved Exercise

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MCQ 1

Statement: The instrument most suitable for measuring the thickness of a few sheets of cardboard is:
Options:
(a) Metre rule
(b) Measuring tape
(c) Vernier Callipers
(d) Micrometer screw gauge
Answer: (d) Micrometer screw gauge
Explanation: A micrometer screw gauge is specifically designed to measure very small thicknesses, such as the thickness of thin materials like sheets of cardboard, with high precision.

MCQ 2

Statement: One femtometre is equal to:
Options:
(a) 10−9 m
(b) 1015 m
(c) 10−15 m
(d) 105 m
Answer: (c) 10−15 m
Explanation: A femtometre (fm) is a unit of length equal to 10−15 metres, commonly used in nuclear physics to measure distances at the subatomic level.

MCQ 3

Statement: A light year is a unit of:
Options:
(a) Light
(b) Time
(c) Distance
(d) Speed
Answer: (c) Distance
Explanation: A light year is the distance that light travels in one year in a vacuum, which is approximately 9.46×1012 kilometers.

MCQ 4

Statement: Which one is a non-physical quantity?
Options:
(a) Distance
(b) Density
(c) Colour
(d) Temperature
Answer: (c) Colour
Explanation: Colour is a perceptual property and not a measurable physical quantity like distance, density, or temperature.

MCQ 5

Statement: When using a measuring cylinder, one precaution to take is to:
Options:
(a) Check for the zero error
(b) Look at the meniscus from below the level of the water surface
(c) Take several readings by looking from more than one direction
(d) Position the eye in line with the bottom of the meniscus
Answer: (d) Position the eye in line with the bottom of the meniscus
Explanation: To ensure accurate readings, the observer must position their eye level with the bottom of the meniscus, which is the curved surface of the liquid.

MCQ 6

Statement: Volume of water consumed by you per day is estimated in:
Options:
(a) Millilitre
(b) Litre
(c) Kilogram
(d) Cubic metre
Answer: (b) Litre
Explanation: The volume of water consumption is typically measured in litres, which is a convenient unit for daily use.

MCQ 7

Statement: A displacement can is used to measure:
Options:
(a) Mass of a liquid
(b) Mass of a solid
(c) Volume of a liquid
(d) Volume of a solid
Answer: (d) Volume of a solid
Explanation: A displacement can is used to measure the volume of an irregularly shaped solid by observing the amount of liquid it displaces.

MCQ 8

Statement: Two rods with lengths 12.321 cm and 10.3 cm are placed side by side, the difference in their lengths is:
Options:
(a) 2.02 cm
(b) 2.0 cm
(c) 2.021 cm
(d) 2.021 cm
Answer: (b) 2.0 cm
Explanation: The difference in length is calculated as 12.321−10.3=2.021, but the result is rounded off to 2.02.0 cm based on the significant figures.

MCQ 9

Statement: Which of the following measures are likely to represent the thickness of a sheet of this book?
Options:
(a) 6×10−56 m
(b) 1×10−41 m
(c) 1.2×10−15 m
(d) 4×10−24 m
Answer: (b) 1×10−41 m
Explanation: The thickness of a sheet of paper in a book is typically in the range of 10−4 meters, equivalent to 0.1 mm.

1.1 Can a non-physical quantity be measured? If yes, then how?

No, a non-physical quantity, such as emotions, feelings, or color, cannot be measured directly because they are not tangible. However, we can assess them indirectly through surveys, psychological methods, or other qualitative approaches.

1.2 What is measurement? Name its two parts.

Measurement is the process of comparing an unknown quantity with a standard quantity of the same kind. The two parts of a measurement are:

  1. Numerical value (indicates the magnitude).
  2. Unit (specifies the standard of measurement, e.g., meters, kilograms).

1.3 Why do we need a standard unit for measurements?

We need standard units to ensure consistency, reliability, and uniformity in measurements. Without standard units, comparing and sharing results across different places or systems would become difficult and confusing.

1.4 Write the names of three base quantities and three derived quantities.

Base quantities:

  1. Length
  2. Mass
  3. Time

Derived quantities:

  1. Speed (derived from length/time)
  2. Volume (derived from length³)
  3. Force (derived from mass × acceleration).

1.5 Which SI unit will you use to express the height of your desk?

The height of a desk is typically expressed in meters (m) or centimeters (cm), depending on its size.

1.6 Write the names and symbols of all SI base units.

  1. Length: Meter (m)
  2. Mass: Kilogram (kg)
  3. Time: Second (s)
  4. Electric current: Ampere (A)
  5. Temperature: Kelvin (K)
  6. Amount of substance: Mole (mol)
  7. Luminous intensity: Candela (cd)

1.7 Why is a prefix used? Name three sub-multiples and three multiples with their symbols.

Why prefixes are used: Prefixes are added to SI units to express very large or very small quantities in a convenient way, avoiding the need for many zeros.

Sub-multiples:

  1. Milli (m) = 10−3
  2. Micro (µ) = 10−6
  3. Nano (n) = 10−9

Multiples:

  1. Kilo (k) = 103
  2. Mega (M) = 106
  3. Giga (G) = 109

1.8 What is meant by:

(a) 55 pm = 5×10−12 meters (picometers, used to measure atomic distances).
(b) 1515 ns = 15×10−9 seconds (nanoseconds, used for time intervals in electronics).
(c) 66 µm = 6×10−6 meters (micrometers, used for measuring microscopic distances).
(d) 55 fs = 5×10−15 seconds (femtoseconds, used in ultrafast phenomena).

1.9 For what purpose is a Vernier Callipers used?

A Vernier Callipers is used to measure:

  1. The external dimensions of an object (e.g., diameter of a cylinder).
  2. The internal dimensions of an object (e.g., diameter of a hole).
  3. The depth of an object.

Main parts:

  • Main scale
  • Vernier scale

How least count is found:
The least count is calculated as: Least count=Smallest division on main scale/Total number of divisions on Vernier scale

1.10 State least count and Vernier scale reading as shown in the figure and hence find the length.

Least count: Assume the smallest division on the main scale is 1 mm and there are 10 divisions on the Vernier scale. Least count=110=0.1 mm

Vernier scale reading: Check the alignment of the Vernier and main scale; the reading will be calculated as: Length=Main scale reading+(Vernier division×Least count).

(Values can be estimated based on the image provided.)

1.11 Which reading out of A, B, and C shows the correct length and why?

The correct length is the one where the zero of the Vernier scale aligns perfectly with the reading on the main scale. (Specific answer depends on analyzing the given figure in detail.)

C.1.1 In what unit will you express each of the following?

(a) Thickness of a five-rupee coin:
The thickness of a coin is small, so it is best measured in millimeters (mm) or micrometers (µm) for greater precision.

(b) Length of a book:
The length of a book can be expressed in centimeters (cm) or millimeters (mm), depending on the level of detail required.

(c) Length of a football field:
A football field is large, so its length is expressed in meters (m) or sometimes in yards (if using non-metric units).

(d) The distance between two cities:
The distance between two cities is usually measured in kilometers (km) because the distance is large.

(e) Mass of a five-rupee coin:
The mass of a coin is small, so it is measured in grams (g) or milligrams (mg) for high precision.

(f) Mass of your school bag:
The mass of a school bag is measured in kilograms (kg) because it is heavier than smaller objects like a coin.

(g) Duration of your class period:
The duration of a class period is expressed in minutes (min) or hours (h).

(h) Volume of petrol filled in the tank of a car:
The volume of petrol is expressed in litres (L), which is the standard unit for liquid volumes.

(i) Time to boil one litre of milk:
The time to boil milk is usually measured in minutes (min) or seconds (s), depending on how precise the timing is.

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