Publisher |
: Santra publication pvt. ltd |

Book Name |
: Madhyamik Physical Science And Environment |

Class |
: 9 (Madhyamik) |

Subject |
: Physical Science |

Chapter Name |
: Measurement |

Table of Contents

Toggle**Multiple choice questions (MCQ)**

**Question 1**

**If u = unit, n = magnitude, then the measurement is**

**n/u****n**^{2}u**nu****n+u**

**Answer**

(c) nu

**Question 2**

**Which one of the following is not a physical quantity?**

**mass****volume****pleasure****length**

**Answer**

(c) pleasure

**Question 3**

**What is the dimensional formula of force?**

**[M°LT**^{-1}]**[MLT**^{-2}]**[ML**^{2}T^{-2}]**[ML**^{-1}T^{-2}]

**Answer**

^{-2}]

**Question 4**

**One astronomical unit (AU) is the average distance between**

**The sun and the moon****The Earth and the moon****The Earth and the sun****None of these**

**Answer**

the Earth and the Sun

**Explanation**

An astronomical unit (AU) is a unit of measurement used in astronomy to represent distances within the Solar System. It is defined as the average distance between the Earth and the Sun, which is approximately 149.6 million kilometres (93 million miles) or 1 astronomical unit (AU).

**Question 5**

**What is the least count of a linear meter scale?**

**1 cm****0.01 cm****0.1 cm****0.001 cm**

**Answer**

1 mm or 0.1 cm

**Explanation**

The least count of a measuring instrument is the smallest value that can be measured with that instrument. In the case of a linear meter scale, the smallest division or graduation on the scale is typically 1 mm.

**Question 6**

**1 Å is equal to**

**10**^{-6}m**10**^{-8}m**10**^{-10}m**10**^{8}m

**Answer**

10^{-10} m

**Explanation**

The angstrom is a unit of length commonly used in chemistry and physics to express atomic dimensions and bond lengths. One angstrom is equal to 10^-10 meters, or one ten-billionth of a meter.

**Question 7**

**Which one of the following is the fundamental/ basic unit?**

**light year****kg.m/s****kg/m**^{3 }**newton**

**Answer**

light year

**Question 8**

**Which one is a quantity with unit but without dimension?**

**pressure****velocity****solid angle****area**

**Answer**

Solid angle

**Explanation**

Solid angle is a quantity with unit but without dimension.

**Question 9**

**How many km are there in one light year?**

**9.46 × 10**^{15}**9.46 × 10**^{12}**9.46 × 10**^{9}**9.46 × 10**^{6}

**Answer**

9.46 × 10^{12}

**Explanation**

To convert from light years to kilometres, we can use the speed of light as a conversion factor. The speed of light is approximately 299,792.458 kilometres per second. Therefore, we can calculate the distance in kilometres that light travels in one year as follows:

1 light year = (299,792.458 km/s) × (60 s/min) × (60 min/hr) × (24 hr/day) × (365.25 days/year)

Simplifying this expression, we get:

1 light year ≈ 9.46 × 10^{12} km

Therefore, there are approximately 9.46 × 10^{12} kilometres in one light year.

**Question 10**

**Unit of temperature in the SI system is**

**°K****K****°F****°C**

**Answer**

K

**Explanation**

The unit of temperature in the SI system is K (Kelvin).

**Answer in one word or in one sentence **

**[Each of Marks 1]**

**Question 2**

**Which quantity has the unit of m/s**^{2}?**Acceleration has the unit (in SI system) ms**^{-2}. Is it a base unit?**Which quantity has the dimension [MLT**^{-1}]?**The light year represents which quantity?****Mention the unit of electric/current.****Write down the CGS unit of momentum, pressure, and force.****Write down the SI unit of momentum, pressure, and force.****Which one is a scalar quantity? Speed or velocity?****What is the least count of an instrument?****What is the dimensional formula of force?**

**Answer**

- Acceleration
- No, it is a derived unit.
- Momentum
- Distance
- Ampere
- g.cm/s, dyn/cm², dyn
- kg.m/s, Pa, N
- Speed
- The smallest value that can be measured with that instrument is called
**least count.** - [M L T
^{-2}]

## Short Answer Question

**[Each of Marks 2]**

**Question 1**

**What is the least count? Mention an instrument having the least count of 1 mm. **

**Answer**

The least count of an instrument is the smallest measurement that can be made with that instrument. An instrument with the least count of 1 mm is a linear scale.

**Question 2**

**Define the terms: oscillation, frequency and time period in relation to the simple pendulum. **

**Answer**

- Oscillation refers to the back and forth motion of a pendulum.
- Frequency is the number of oscillations per unit of time (usually measured in hertz).
- Time period is the duration of one complete oscillation.

**Question 3**

**When a pendulum is taken to the moon, explain whether the time period will increase or decrease. **

**Answer**

The time period of a pendulum on the moon would increase. This is because the force of gravity on the moon is weaker than on the Earth.

**Question 4**

**Write the name of the instrument used to measure the mass and state its principle. **

**Answer**

An instrument used to measure mass is a common balance. The principle of balance is based on the equilibrium of forces between the object being weighed and a set of standard weights.

**Question 5**

**If one measures the length of an object to be 2.70 mm with an instrument of least count 0.01 mm. What is the percentage error in the measurement?**

**Answer**

The percentage error in the measurement

= (0.01 mm/2.70 mm) × 100%

= 0.37%.

**Question 6**

**Explain which one is the most accurate measurement. (a) 2000 g, (b) 2.0 kg, (c) 2.00 kg, (d) 2 kg**

**Answer**

The most accurate measurement is 2000 g, as it has the most number of significant figures, and therefore the least uncertainty.

**Question 7**

**Name two kinds of error in a measurement. How are they minimized? **

**Answer**

The two kinds of errors in measurement are systematic errors and random errors. Systematic errors arise from flaws in the measuring instrument or the experimental setup, while random errors arise from the natural measurement variability.

**Question 8**

**How does the percentage error depend on the least count? Explain with an example. **

**Answer**

The percentage error is inversely proportional to the least count. This means that as the least count decreases, the percentage error increases. For example, an instrument with a least count of 0.1 mm will have a higher percentage error than an instrument with a least count of 1 mm.

**Question 9**

**Explain precision and accuracy. **

**Answer**

Precision refers to the reproducibility or consistency of measurements.

Accuracy refers to the closeness of a measurement to the true or accepted value.

**Question 10**

**What is the maximum possible error in the measurement of 1.60 cm? Explain.**

**Answer**

The maximum possible error in the measurement of 1.60 cm would be half the least count of the instrument used to measure it. If the least count is 0.1 cm, then the maximum possible error would be 0.05 cm.

## Long Answer Question

**[Each of Marks 3]**

**Question 1**

**Explain: Physical quantity, unit. Give examples.**

**Answer**

A physical quantity is any measurable property of a physical system. A unit is a standardized way to express the magnitude of a physical quantity. Examples of physical quantities include mass, time, length, temperature, and electric current, while examples of units include meters (m), seconds (s), and kilograms (kg).

**Question 2**

**Explain with an example that a quantity may be unitless. **

**Answer**

A quantity may be unitless if it is a ratio of two physical quantities with the same units that cancel each other out. For example, the coefficient of friction is a unitless quantity since it is the ratio of the force of friction (in Newtons, N) to the normal force (also in N), which cancels each other out.

**Question 3**

**Explain with an example: Fundamental and derived unit. **

**Answer**

Fundamental units are the basic units of measurement for fundamental physical quantities, such as the meter (m) for length or the kilogram (kg) for mass.

Derived units are formed by combining fundamental units, such as the unit for speed, which is meters per second (m/s), or the unit for force, which is Newton (N) derived from the fundamental units of mass, length, and time.

**Question 4**

**Explain what do you mean by standard length and standard time. **

**Answer**

The standard length refers to a fixed distance that serves as a reference for measurements of length. The most widely accepted standard length is the international prototype of the meter, which is a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France.

Standard time refers to a universally agreed-upon method of measuring time, which is used as a reference for timekeeping around the world. The most widely used standard time is Coordinated Universal Time (UTC), which is based on atomic clocks and is used as the basis for time zones and global communication.

**Question 5**

**Mention the relation between different units of volume: 1L, 1 m ^{3}, 1 mL, 1 cm^{3}, 1 dm^{3}. **

**Answer**

1 m³ = 1,000,000 cm³ = 1,000 dm³ = 1,000 L

1 L = 1,000 mL

1 cm³ = 1 mL

1 dm³ = 1 L

**Question 6**

**Why temperature has to be mentioned while defining 1 L? **

**Answer**

Temperature has to be mentioned when defining 1 L because the volume of a substance is affected by its temperature due to thermal expansion. The definition of 1 L assumes a specific temperature of 273.15 K and a pressure of 1 atm, so it is important to specify these conditions.

**Question 7**

**Mention two units for each for measuring objects of size (i) very large (ii) very small. Why do you require units of different sizes? **

**Answer**

- Two units for measuring objects of a size that are very large are kilometres (km) and astronomical units (AU). Kilometres are used for measuring distances on Earth, while astronomical units are used to measure distances between celestial objects.
- Two units for measuring objects of a size that are very small are nanometers (nm) and angstroms (Å). Nanometers are used to measure the size of small particles such as atoms and molecules, while angstroms are used for measuring atomic and molecular distances.

Units of different sizes are required because different objects or phenomena have vastly different sizes and scales. For example, the size of an atom is much smaller than the size of a cell, which is much smaller than the size of a human, and so on. Using the appropriate unit of measurement allows us to express these sizes in a meaningful way that is appropriate for the scale of the object or phenomenon being measured.

**Question 8**

**Explain with example: dimensional formula and dimensional equation. **

**Answer**

The dimensional formula expresses a physical quantity in terms of its fundamental dimensions. For example, the dimensional formula for velocity is [L T^{-1}], which means it has dimensions of length per unit time.

The dimensional equation relates the dimensions of physical quantities in an equation. For example, the dimensional equation for velocity is V = [L T^{-1}], which means that the velocity V is equal to a quantity with dimensions of length per unit time.

**Question 9**

**Define (i) 1 joule, (ii) 1 newton, (iii) 1 nanosecond, (iv) 1 light year, (v) 1 μ, (vi) 1Å, (vii) 1 u (or amu). **

**Answer**

- 1 joule is the amount of work done when a force of 1 newton is applied over a distance of 1 meter in the direction of the force.
- 1 newton is the force required to accelerate a mass of 1 kilogram at a rate of 1 meter per second squared.
- 1 nanosecond is a unit of time equal to one billionth of a second (10
^{-9}seconds). - 1 light year is the distance that light travels in one year, approximately equal to 9.46 trillion kilometres.
- 1 μ (or micrometre) is a unit of length equal to one-millionth of a meter (10
^{-6}meters). - 1 Å (or angstrom) is a unit of length equal to one ten-billionth of a meter (10
^{-10}meters). - 1 u (or amu) is a unit of mass equal to one-twelfth of the mass of a carbon-12 atom, approximately equal to 1.66 × 10
^{-27}kilograms.

**Question 10**

**The typical length of a bacteria is 0.5 μ. How many bacteria are there in 1 m length? [Ans. 2 × 10 ^{6}]**

**Answer**

Length of a bacteria = 0.5 μm

We need to find the number of bacteria in 1 m length.

We can start by converting the length of a bacteria from micrometres to meters:

0.5 μm = 0.5 × 10^{-6} m

Next, we can divide the total length of 1 m by the length of a single bacteria in meters:

Number of bacteria in 1 m = 1 \over 0.5 × 10^{-6}

Number of bacteria in 1 m = 2 × 10^{6} bacteria

Therefore, there are 2 × 10^{6} bacteria in 1 m length.