IGCSE Practice Questions: Physical Quantities, Scalars, and Errors
### Physical Quantities and SI Units
1. Which of the following is a base quantity in the SI system?
a) Speed b) Mass c) Force d) Pressure
Answer: b) Mass
Explanation: Mass is a base quantity; speed, force, and pressure are derived from base quantities.
2. What is the SI unit of time?
a) Hour b) Minute c) Second d) Day
Answer: c) Second
Explanation: The SI unit for time is the second (s).
3. Which unit is not an SI unit?
a) Kilogram b) Kelvin c) Liter d) Ampere
Answer: c) Liter
Explanation: Liter is a non-SI unit; the SI unit for volume is the cubic meter (m^3).
4. How is 1 newton defined in SI base units?
a) kg·m/s^2 b) m^2/s
c) kg·m^2/s^2 d) kg·s^2/m
Answer: a) kg·m/s^2
Explanation: Force is defined as mass * acceleration (F = ma).
5. What is the prefix for 10-^3?
a) Mega b) Milli c) Micro d) Nano
Answer: b) Milli
Explanation: Milli (m) represents 10-^3.
6. Which physical quantity is measured in joules?
a) Force b) Work c) Power d) Pressure
Answer: b) Work
7. Convert 0.005 kilometers to meters.
a) 0.5 m b) 5 m c) 50 m d) 500 m
Answer: b) 5 m
Explanation: 1 kilometer = 1000 meters; 0.005 * 1000 = 5.
8. What is the SI unit for electric charge?
a) Coulomb b) Ampere c) Volt d) Ohm
Answer: a) Coulomb
Explanation: Electric charge is measured in coulombs (C).
9. Which of these is a vector quantity?
a) Temperature b) Distance c) Velocity d) Energy
Answer: c) Velocity
Explanation: Velocity has both magnitude and direction, making it a vector.
10. What is the unit for frequency?
a) Hertz
b) Joule c) Watt d) Decibel
Answer: a) Hertz
Explanation: Frequency is measured in hertz (Hz), equivalent to cycles per second.
### Scalars and Vectors
11. Which of the following is a scalar quantity?
a) Displacement b) Speed
c) Acceleration d) Force
Answer: b) Speed
Explanation: Speed has magnitude but no direction, unlike displacement, acceleration, and force.
12. A car travels 40 km east and then 30 km west. What is its displacement?
a) 10 km b) 70 km c) 40 km d) 30 km
Answer: a) 10 km
Explanation: Displacement = 40 - 30 = 10 km (east).
a) Add the magnitudes directly
b) Subtract the smaller vector from the larger vector
c) Use the Pythagorean theorem for perpendicular vectors d) Multiply the magnitudes
Answer: c) Use the Pythagorean theorem for perpendicular vectors Explanation: For perpendicular vectors, resultant = sqrt(A^2 + B^2).
14. Which vector operation gives a scalar quantity?
a) Cross product b) Dot product c) Vector addition d) Vector subtraction Answer: b) Dot product
Explanation: The dot product results in a scalar.
15. What is the direction of the cross product of two vectors?
a) Along the direction of the first vector b) Along the direction of the second vector c) Perpendicular to both vectors
d) In the plane of the two vectors
Answer: c) Perpendicular to both vectors
Explanation: The cross product produces a vector perpendicular to the plane formed by the original vectors.
16. A car moves with a velocity of 20 m/s east for 10 s. What is its displacement?
a) 200 m
b) 20 m c) 2 m d) 0 m
Answer: a) 200 m
Explanation: Displacement = velocity * time = 20 * 10 = 200 m.
17. Which of the following is a property of vectors?
a) Only magnitude
b) Magnitude and direction c) Only direction
d) Magnitude, direction, and unit Answer: b) Magnitude and direction
Explanation: Vectors have both magnitude and direction.
18. What is the unit vector along the x-axis?
a) j b) i c) k
d) None of these Answer: b) i
Explanation: i represents the unit vector along the x-axis.
### Errors and Uncertainties
19. Which of the following describes a systematic error?
a) Fluctuations in measurements due to random factors
c) A one-time error in data recording d) A mistake made in calculation
Answer: b) A consistent error in measurements due to a faulty instrument Explanation: Systematic errors cause consistent bias in results.
20. What is the percentage uncertainty of a measurement 20.0 +/- 0.5 cm?
a) 1.0%
b) 2.5%
c) 5.0%
d) 0.5%
Answer: b) 2.5%
Explanation: Percentage uncertainty = (0.5 / 20.0) * 100 = 2.5%.
