Units and Dimensions: Master the Fundamentals of Measurement

Question 1

What is the numerical value of the prefix "mega"?

Accepted Answer

10^6

Answer

10^3

Answer

10^-3

Answer

10^-6

Question 2

Can dimensional analysis be used to determine the missing term in an equation?

Accepted Answer

Yes

Answer

No

Question 3

Which SI unit is used to measure electric charge?

Accepted Answer

Coulomb

Answer

Ampere

Answer

Volt

Answer

Ohm

Question 4

Which of the following is a derived SI unit?

Accepted Answer

Force

Answer

Meter

Answer

Second

Answer

Temperature

Question 5

What is the dimensional formula for acceleration?

Accepted Answer

L/T^2

Answer

L^2/T^3

Answer

LT^2

Answer

T^2/L

Question 6

Which of the following prefixes represents 10^-3?

Accepted Answer

milli

Answer

micro

Answer

centi

Answer

kilo

Question 7

The fundamental base unit of time in the International System of Units (SI) is the:

Accepted Answer

Second

Answer

Minute

Answer

Hour

Answer

Day

Question 8

The dimensional formula for velocity, which represents the rate of change of displacement with time, is:

Accepted Answer

LT^-1

Answer

MLT^-1

Answer

ML^2T^-2

Answer

LT

Question 9

To check the validity of a physical equation using dimensional analysis, the dimensions on both sides of the equation must be:

Accepted Answer

Identical

Answer

Different

Answer

Approximately equal

Answer

Dimensionless

Question 10

Which of the following is NOT classified as a scalar physical quantity?

Accepted Answer

Force

Answer

Temperature

Answer

Speed

Answer

Mass

Question 11

For accurately measuring the mass of a small object, the most appropriate instrument to use is:

Accepted Answer

Analytical balance

Answer

Spring balance

Answer

Bathroom scale

Answer

Triple beam balance

Question 12

The SI unit for measuring luminous intensity, which quantifies the strength of light emitted from a source, is:

Accepted Answer

Candela

Answer

Lumen

Answer

Lux

Answer

Watt

Question 13

In the International System of Units (SI), the base unit of length is:

Accepted Answer

Meter

Answer

Kilogram

Answer

Second

Answer

Ampere

Question 14

The SI prefix 'kilo-' indicates:

Accepted Answer

10^3

Answer

10^-3

Answer

10^-6

Answer

10^6

Question 15

Which of the following is NOT regarded as a fundamental quantity?

Accepted Answer

Area

Answer

Length

Answer

Time

Answer

Mass

Question 16

Within the SI system, the unit for electric current is the:

Accepted Answer

Ampere

Answer

Volt

Answer

Ohm

Answer

Farad

Question 17

What is the SI base unit for mass?

Accepted Answer

Kilogram

Answer

Meter

Answer

Second

Answer

Ampere

Question 18

Which of the following is a derived SI unit?

Accepted Answer

Joule

Answer

Meter

Answer

Second

Answer

Ampere

Question 19

What is the SI unit for electrical potential difference?

Accepted Answer

Volt

Answer

Ohm

Answer

Ampere

Answer

Coulomb

Question 20

Which of the following is NOT a fundamental dimension?

Accepted Answer

Force

Answer

Mass

Answer

Length

Answer

Time

Question 21

The density of a substance is defined as mass per unit volume. What is the SI unit for density?

Accepted Answer

kg/m^3

Answer

m^3/kg

Answer

kg/m^2

Answer

m^2/kg

Question 22

A capacitor has a capacitance of 10 μF. What is its capacitance in farads?

Accepted Answer

0.001 F

Answer

0.01 F

Answer

1.0 F

Answer

100 F

Question 23

Which of the following units is NOT a fundamental base unit in the International System of Units (SI)?

Accepted Answer

Hertz

Answer

Second

Answer

Meter

Answer

Ampere

Question 24

What is the SI unit of force?

Accepted Answer

Newton

Answer

Watt

Answer

Pascal

Answer

Joule

Question 25

Which of the following equations is dimensionally incorrect?

Accepted Answer

F = m * v^2

Answer

d = v * t

Answer

E = mc^2

Answer

P = V * I

Question 26

What is the order of magnitude of the speed of light in meters per second?

Accepted Answer

10^8

Answer

10^12

Answer

10^6

Answer

10^3

Question 27

Which of the following quantities is a scalar?

Accepted Answer

Temperature

Answer

Velocity

Answer

Force

Answer

Acceleration

Question 28

What is the SI unit of energy?

Accepted Answer

Joule

Answer

Watt

Answer

Coulomb

Answer

Newton

Question 29

Which of the following is a unit of pressure?

Accepted Answer

Pascal

Answer

Farad

Answer

Tesla

Answer

Hertz

Question 30

What is the relationship between the units of force and pressure?

Accepted Answer

Pressure = Force / Area

Answer

Pressure = Force - Area

Answer

Force = Pressure * Area

Answer

Area = Force / Pressure

Question 31

Which of the following is the SI base unit of mass?

Accepted Answer

Kilogram (kg)

Answer

Meter (m)

Answer

Second (s)

Answer

Ampere (A)

Question 32

The prefix 'femto' represents a factor of:

Accepted Answer

10^-15

Answer

10^-12

Answer

10^15

Answer

10^-9

Question 33

Which of the following equations is dimensionally correct?

Accepted Answer

Force = mass × acceleration

Answer

Force = mass × velocity

Answer

Force = velocity × displacement

Answer

Force = acceleration × time

Question 34

The derived SI unit of energy is the:

Accepted Answer

Joule (J)

Answer

Watt (W)

Answer

Hertz (Hz)

Answer

Newton (N)

Question 35

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Electric charge

Answer

Mass

Answer

Temperature

Question 36

The SI unit of magnetic flux density is the:

Accepted Answer

Tesla (T)

Answer

Henry (H)

Answer

Weber (Wb)

Answer

Ampere (A)

Question 37

Which of the following is NOT a base unit in the International System of Units (SI)?

Accepted Answer

Force

Answer

Mass

Answer

Time

Answer

Length

Question 38

What is the correct SI unit for energy?

Accepted Answer

Joule (J)

Answer

Kilogram (kg)

Answer

Newton (N)

Answer

Watt (W)

Question 39

What is the correct prefix for 10^-9?

Accepted Answer

Nano

Answer

Kilo

Answer

Milli

Answer

Micro

Question 40

The equation for the period of a simple pendulum is T = 2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity. What are the dimensions of the period, T?

Accepted Answer

[T]

Answer

[L]

Answer

[LT^-1]

Answer

[M]

Question 41

The equation for the kinetic energy of an object is KE = 1/2mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity. Using dimensional analysis, which of the following equations is dimensionally incorrect?

Accepted Answer

KE = mv

Answer

KE = 1/2mv^2

Answer

KE = 1/2mv^2 + 1/2mv^2

Answer

KE = 1/2mv^2/2

Question 42

A student measures the length of a table to be 1.25 meters. Express this length in centimeters.

Accepted Answer

125 cm

Answer

1.25 cm

Answer

1250 cm

Answer

12.5 cm

Question 43

A car travels at a speed of 60 km/h. What is the car's speed in meters per second (m/s)?

Accepted Answer

16.67 m/s

Answer

100 m/s

Answer

3600 m/s

Answer

60 m/s

Question 44

The density of a substance is calculated by dividing its mass by its volume. What are the dimensions of density?

Accepted Answer

[ML^-3]

Answer

[L^3]

Answer

[LT^-1]

Answer

[M]

Question 45

The volume of a rectangular prism is calculated by multiplying its length, width, and height. What is the volume of a rectangular prism with dimensions of 2 cm x 3 cm x 4 cm?

Accepted Answer

24 cm^3

Answer

9 cm^3

Answer

6 cm^3

Answer

12 cm^3

Question 46

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius. What are the dimensions of area?

Accepted Answer

[L^2]

Answer

[L]

Answer

[T]

Answer

[L^3]

Question 47

Which of the following is NOT a base unit in the International System of Units (SI)?

Accepted Answer

Volume

Answer

Mass

Answer

Time

Answer

Length

Question 48

What is the correct prefix for 10^-9?

Accepted Answer

nano

Answer

micro

Answer

milli

Question 49

What is the dimension of force?

Accepted Answer

MLT-2

Answer

ML-1T-2

Answer

ML2T-2

Answer

MLT-1

Question 50

Which of the following equations is dimensionally incorrect?

Accepted Answer

Distance = Speed x Time²

Answer

Speed = Distance / Time

Answer

Force = Mass x Acceleration

Answer

Acceleration = Change in Velocity / Time

Question 51

The density of a substance is 2.5 g/cm³. What is its density in kg/m³?

Accepted Answer

2500 kg/m³

Answer

250 kg/m3

Answer

25 kg/m3

Answer

0.25 kg/m³

Question 52

Which of the following is NOT a valid unit for energy?

Accepted Answer

Newton-meter/second

Answer

Kilowatt-hour

Answer

Joule

Answer

Electronvolt

Question 53

A student measures the length of a table to be 1.50 meters. The uncertainty in the measurement is ±0.05 meters. What is the percentage uncertainty in the measurement?

Accepted Answer

3.3%

Answer

5.0%

Answer

0.05%

Question 54

Which of the following pairs of quantities has the same dimensions?

Accepted Answer

Energy and Work

Answer

Force and Pressure

Answer

Velocity and Acceleration

Answer

Momentum and Impulse

Question 55

A student derives an equation for the period of a pendulum, T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. Using dimensional analysis, what is the dimension of the expression √(L/g)?

Accepted Answer

T

Answer

LT-2

Answer

L