Chapter 1 – Measurements | Chapter Solution Class 9

The word ‘Science’ originated from the Latin word ‘Scientia’, which means ‘to know’.

The word ‘Physics’ comes from the Greek word ‘Physis’, which means ‘nature’.

Anything that can be measured is called a physical quantity. For example, length, mass, volume, and time are all physical quantities.

Scalar Quantity – Physical quantities that have only magnitude and no direction.

Vector Quantity – Physical quantities that have both magnitude and direction.

• CGS System (Centimeter-Gram-Second System)
• SI System (International System of Units)

The SI unit of electric current is Ampere (A).

There are seven fundamental units in the SI system.

An Astronomical Unit (AU) is used to measure the mean distance between the Earth and the Sun.

No, parsec (pc) is not a unit of time. It is a unit of distance used in astronomy.

The dimension of area is [L²].

A measuring cylinder is used to measure the volume of a liquid or irregular solid using the displacement method.

A Spring Balance is used to measure the weight of a body.

A stopwatch is used to measure small time intervals accurately, often up to one-tenth of a second.

The multiplicative factor of micro (μ) is 10⁻⁶.

The dimension of area is [L²].

A common balance is used to measure the mass of a body by comparing it with standard weights.

A unit is a standard quantity used to express a physical quantity.

Importance of Units in Measurement:

• Units help compare measurements.
• Without units, measurements become meaningless.
• Example: Saying “length is 5” is unclear, but “length is 5 cm” is meaningful.

Fundamental Units:

• Units that are independent and cannot be derived from other units.
• Example: meter (m) for length, kilogram (kg) for mass, second (s) for time.

Derived Units:

• Units obtained from fundamental units.
• Example: Newton (N) = kg·m/s² (force), Joule (J) = kg·m²/s² (energy).

CGS System (Centimeter-Gram-Second System):

• Used in scientific measurements.
• Length in centimeters (cm), mass in grams (g), time in seconds (s).

SI System (International System of Units):

• Globally accepted system of measurement.
• Length in meters (m), mass in kilograms (kg), time in seconds (s), and includes electric current (A), temperature (K), luminous intensity (cd), and mole (mol).

The C.G.S. system is simple and widely used in scientific experiments. It is convenient for measuring small quantities, such as in physics and chemistry labs. The system uses centimeters, grams, and seconds, making calculations easier for small-scale measurements compared to the M.K.S. or SI system.

The mass of a body is measured using a common balance by comparing it with standard weights. A spring balance measures weight based on gravity. The SI unit of mass is the kilogram (kg), while grams (g) are used for smaller measurements in the C.G.S. system.

A pendulum clock has a pendulum that swings, regulating time. A seconds pendulum has a 2-second time period.

A stopwatch is used for measuring short time intervals and works with a knob to start/stop. It can measure time up to one-tenth of a second accurately.

Yes, derived units are formed using fundamental units.

Example:

• Velocity (m/s) uses length (m) and time (s)
• Force (N) uses mass (kg), length (m), and time (s²).

An ordinary scale is a thin rectangular strip made of wood, plastic, or metal.

A straight line is measured by aligning the scale correctly.

Parallax error occurs when the eye is not placed perpendicular to the reading, causing incorrect measurements. It is avoided by proper eye positioning.

A pendulum clock has a pendulum that swings, regulating time. A seconds pendulum has a 2-second time period. A stopwatch is used for measuring short time intervals and works with a knob to start/stop. It can measure time up to one-tenth of a second accurately.

Weights in a weight box follow the 1:2:2:5 ratio to allow precise measurement combinations. This arrangement ensures any weight within the box’s range can be measured accurately using different combinations of standard weights, making it efficient for balancing measurements.

Light Year: A light year (ly) is the distance travelled by light in one year in a vacuum. 1 ly = 9.46 × 10¹⁵ m.

Astronomical unit: An astronomical unit (AU) is the average distance between the Earth and the Sun. 1 AU =  1.5 × 10¹¹ m.

A parsec (pc) is 3.26 light-years or 3.08 × 10¹⁶ m, used in astronomy for large distances.

A micron (μm) is 10⁻⁶ meters, used for measuring microscopic objects like bacteria or dust particles.

The dimensions of a physical quantity are the powers to which fundamental quantities like mass, length, and time are raised to represent the quantity.

Dimension of velocity: [L¹T⁻¹]

Dimension of acceleration: [L¹T⁻²]

Fold the paper multiple times until the thickness is measurable. Measure the total thickness (x) using a linear scale. Divide it by the number of folds (n) to find the thickness of a single sheet using the formula:

Thickness = x/n

Find the mass (m) of the stone using a spring balance.

Measure the volume (V₂ – V₁) by immersing the stone in a measuring cylinder filled with water.

Use the formula: Density = \text{m}\over \text{V₂ - V₁}

(i) The word science originated from the Latin word Scientia.

(ii) Atomic weight is the ratio of two weights.

(iii) The light year is the unit of distance.

(iv) [MLT⁻²] is the dimension of force.

(v) Small time intervals are measured by a stopwatch.

False

Explanation: The word ‘Physis’ comes from Greek and means ‘nature’, not science. Physics, derived from this term, is the branch of science that studies nature and natural phenomena.

False

Explanation: The SI unit of solid angle is steradian (sr), while radian (rad) is the unit of plane angles.

False

Explanation:

A parsec (pc) is a unit of distance, equal to 3.26 light-years or 3.08 × 10¹⁶ meters, used to measure vast astronomical distances.

True

Explanation:

A spring balance measures weight, which is the force exerted by gravity on an object. The scale reading is in Newtons (N), the unit of force.

(b) kg

Explanation:

The SI unit of mass is kilogram (kg). The CGS system uses grams (g), while larger units like quintal and ton are non-SI units used for heavier masses.

(c) newton

Explanation:

Weight is the force of gravity acting on an object. Since force is measured in Newtons (N) (1 N = kg·m/s²), the correct answer is Newton. Dyne is a smaller unit of force in the CGS system.

(c) ampere

Explanation:

A fundamental unit is one that is independent and not derived from other units. Ampere (A) is the SI unit of electric current. Newton (N) is a derived unit of force, while litre (L) and coulomb (C) are also derived units.

(c) distance

Explanation:

A light year is the distance that light travels in one year in a vacuum, approximately 9.46 × 10¹⁵ meters. It is used in astronomy to measure large distances.

(b) square root of its length

Explanation:

The time period (T) of a simple pendulum is given by

T = 2π √(l/g)

where L is the length of the pendulum and g is acceleration due to gravity. This shows that T is proportional to the square root of L.

(a) 7

Explanation: The SI system has seven fundamental units:

• Length (metre, m)
• Mass (kilogram, kg)
• Time (second, s)
• Electric current (ampere, A)
• Temperature (kelvin, K)
• Luminous intensity (candela, cd)
• Amount of substance (mole, mol)

(d) 10⁶

Explanation:

Mega (M) is a prefix used in the SI system that represents 10⁶ (1,000,000). For example, 1 megawatt (MW) = 10⁶ watts.

(b) 10⁻³ m³

Explanation:

• 1 litre (L) = 1000 cm³ = 10⁻³ m³
• It is a derived unit used for measuring volume, especially for liquids.

(d) [MLT⁻²]

Explanation:

According to Newton’s Second Law, force (F) is defined as mass × acceleration.

Since acceleration is L/T²,

we get F = M × L/T²

= [MLT⁻²]

(a) mass/volume

Explanation:

Density (ρ) is defined as mass per unit volume, represented by ρ = m/V. The SI unit of density is kg/m³.