Chapter -1.1 "Physical quantities and measurement techniques" - MCQ;s
1.1 Physical Quantities and Measurement Techniques - MCQ's
Q1. What is the SI unit of length?
A) Centimetre
B) Millimetre
C) Metre
D) Kilometre
Answer: C) Metre
Explanation:
The SI unit of length is the metre (m). Other units like cm and mm are derived from it.
Q2. The smallest division on a ruler is 1 mm. What is the uncertainty?
A) ±1 mm
B) ±0.5 mm
C) ±0.1 mm
D) ±2 mm
Answer: B) ±0.5 mm
Explanation:
Uncertainty is half the smallest division. Since smallest division is 1 mm, uncertainty is ±0.5 mm.
Q3. Parallax error occurs when:
A) The ruler is broken
B) The object moves
C) The eye is not level with the scale
D) The ruler is dirty
Answer: C) The eye is not level with the scale
Explanation:
Parallax error happens when the measurement is read from an angle rather than directly above the mark.
Q4. A student measures from 1.0 cm to 6.8 cm. What is the length?
A) 7.8 cm
B) 5.8 cm
C) 6.8 cm
D) 5.0 cm
Answer: B) 5.8 cm
Explanation:
Length = Final − Initial
6.8 − 1.0 = 5.8 cm
Q5. Why measure 20 sheets of paper instead of one?
A) To save time
B) To increase thickness
C) To reduce percentage error
D) To avoid parallax
Answer: C) To reduce percentage error
Explanation:
Measuring multiple sheets increases measured value, reducing percentage uncertainty.
Q6. The length of a pendulum is measured from:
A) Pivot to bottom of bob
B) Pivot to centre of bob
C) Top of string to bottom
D) Centre of bob to floor
Answer: B) Pivot to centre of bob
Explanation:
Pendulum length is measured from pivot to centre of mass of the bob.
Q7. Which unit is most suitable for measuring thickness of a coin?
A) m
B) km
C) mm
D) kg
Answer: C) mm
Explanation:
Small lengths are best measured in millimetres.
Q8. A ruler measures up to 30 cm. What is this in metres?
A) 0.03 m
B) 0.3 m
C) 3 m
D) 30 m
Answer: B) 0.3 m
Explanation:
30 cm ÷ 100 = 0.3 m
Q9. Which reduces random error?
A) One reading
B) Estimation
C) Repeating measurements
D) Guessing
Answer: C) Repeating measurements
Explanation:
Taking repeated readings and averaging reduces random error.
Q10. What happens if you read a ruler from below eye level?
A) Reading too small
B) Reading too large
C) No effect
D) Scale changes
Answer: B) Reading too large
Explanation:
Viewing from below shifts apparent position upward, giving larger reading.
Q11. What unit is used for volume in laboratory cylinders?
A) m
B) mL
C) kg
D) N
Answer: B) mL
Explanation:
Volume is measured in millilitres (mL) or cubic centimetres (cm³).
Q12. 1 cm³ is equal to:
A) 1 mL
B) 10 mL
C) 100 mL
D) 0.1 mL
Answer: A) 1 mL
Explanation:
1 cubic centimetre equals 1 millilitre.
Q13. The meniscus should be read at:
A) Top
B) Middle
C) Bottom
D) Any point
Answer: C) Bottom
Explanation:
For water, read bottom of curved surface.
Q14. Why place cylinder on flat surface?
A) To increase volume
B) To avoid spilling
C) For accurate reading
D) To cool liquid
Answer: C) For accurate reading
Explanation:
Tilting changes reading and introduces error.
Q15. Water level changes from 40 mL to 57 mL. What is object volume?
A) 17 mL
B) 97 mL
C) 40 mL
D) 57 mL
Answer: A) 17 mL
Explanation:
Volume = 57 − 40 = 17 mL
Q16. Which method measures irregular solid volume?
A) Formula method
B) Density formula
C) Water displacement
D) Balance method
Answer: C) Water displacement
Explanation:
Irregular shapes cannot use formula, so displacement is used.
Q17. Smallest division is 2 mL. Uncertainty is:
A) ±2 mL
B) ±1 mL
C) ±0.5 mL
D) ±4 mL
Answer: B) ±1 mL
Explanation:
Uncertainty = half smallest division.
Q18. Air bubbles in water cause volume to appear:
A) Smaller
B) Larger
C) Same
D) Negative
Answer: B) Larger
Explanation:
Air bubbles increase displaced volume reading.
Q19. Best cylinder for measuring 12 mL accurately:
A) 250 mL
B) 100 mL
C) 50 mL
D) 10 mL
Answer: D) 10 mL
Explanation:
Smaller cylinder gives better precision.
Q20. Percentage error formula is:
A) Value ÷ Error × 100
B) Error ÷ Value × 100
C) Value × Error
D) Error + Value
Answer: B) Error ÷ Value × 100
Explanation:
Percentage error = (Uncertainty / Measured value) × 100
Q21. A 5 cm object measured with ±0.5 mm uncertainty. What is percentage error?
0.5 mm = 0.05 cm
Percentage error = (0.05 ÷ 5) × 100 = 1%
A) 10%
B) 5%
C) 1%
D) 0.1%
Answer: C) 1%
Q22. Measuring 10 sheets instead of 1 reduces percentage error because:
A) Uncertainty decreases
B) Value increases
C) Scale improves
D) Units change
Answer: B) Value increases
Explanation:
Uncertainty stays same, but measured value increases so percentage error decreases.
Q23. A student reads the top of meniscus. Reading is:
A) Correct
B) Smaller
C) Larger
D) Negative
Answer: C) Larger
Explanation:
Top reading overestimates volume.
Q24. Which instrument measures volume directly?
A) Ruler
B) Vernier
C) Measuring cylinder
D) Balance
Answer: C) Measuring cylinder
Q25. Why repeat measurements?
A) To impress examiner
B) To increase scale
C) To improve reliability
D) To change answer
Answer: C) To improve reliability
Q26. What is the SI unit of time?
A) Minute
B) Hour
C) Second
D) Millisecond
Answer: C) Second
Explanation:
The SI base unit of time is the second (s). All other units such as minutes and hours are derived from seconds.
Q27. Which instrument is most suitable for timing a pendulum experiment in a school lab?
A) Measuring cylinder
B) Stopwatch
C) Ruler
D) Balance
Answer: B) Stopwatch
Explanation:
A stopwatch is designed to measure time intervals and is commonly used for pendulum experiments.
Q28. Why is a digital timer more accurate than a stopwatch?
A) It is bigger
B) It is electronic
C) It removes reaction time error
D) It is more expensive
Answer: C) It removes reaction time error
Explanation:
Digital timers can be connected to sensors, eliminating human reaction time delay.
Q29. A pendulum takes 50 s to complete 25 oscillations. What is the period?
A) 2 s
B) 25 s
C) 0.5 s
D) 75 s
Answer: A) 2 s
Explanation:
Period = Total time ÷ Number of oscillations
Period = 50 ÷ 25 = 2 s
Q30. Why should several oscillations be timed instead of one?
A) To increase speed
B) To reduce percentage uncertainty
C) To make experiment longer
D) To increase amplitude
Answer: B) To reduce percentage uncertainty
Explanation:
Timing multiple oscillations increases the total measured time, reducing percentage uncertainty.
Q31. If one oscillation takes 1.5 s, what is the frequency?
A) 1.5 Hz
B) 0.67 Hz
C) 2 Hz
D) 3 Hz
Answer: B) 0.67 Hz
Explanation:
Frequency = 1 ÷ Period
Frequency = 1 ÷ 1.5 = 0.67 Hz
Q32. Reaction time mainly causes which type of error?
A) Systematic error
B) Zero error
C) Random error
D) Calibration error
Answer: C) Random error
Explanation:
Reaction time varies each time, so it introduces random error.
Q33. A student times 10 oscillations in 15 s. What is the period?
A) 1.5 s
B) 15 s
C) 0.67 s
D) 25 s
Answer: A) 1.5 s
Explanation:
Period = 15 ÷ 10 = 1.5 s
Q34. Which reduces reaction time error?
A) Using larger amplitude
B) Timing one oscillation
C) Using digital timer with sensor
D) Guessing
Answer: C) Using digital timer with sensor
Explanation:
Sensors start and stop timing automatically, removing human delay.
Q35. A stopwatch reads to 0.01 s. What is its approximate uncertainty?
A) ±0.1 s
B) ±0.01 s
C) ±1 s
D) ±0.5 s
Answer: B) ±0.01 s
Explanation:
Uncertainty is approximately equal to the smallest division.
Q36. Why should the pendulum swing at a small angle?
A) To increase speed
B) To keep period constant
C) To reduce mass
D) To increase time
Answer: B) To keep period constant
Explanation:
Large angles may slightly affect the period. Small angles give more consistent results.
Q37. A student measures 5 s for one oscillation. Uncertainty is ±0.2 s. What happens if 10 oscillations are measured instead?
A) Uncertainty increases
B) Percentage uncertainty decreases
C) Period changes
D) Oscillations increase
Answer: B) Percentage uncertainty decreases
Explanation:
Total time increases but uncertainty stays similar, so percentage uncertainty decreases.
Q38. 1 minute equals how many seconds?
A) 100
B) 360
C) 60
D) 600
Answer: C) 60
Explanation:
1 minute = 60 seconds.
Q39. Which quantity depends directly on time measurement?
A) Mass
B) Speed
C) Density
D) Volume
Answer: B) Speed
Explanation:
Speed = Distance ÷ Time.
Q40. If total time for 20 oscillations is 30 s, what is the period?
A) 1.5 s
B) 0.67 s
C) 10 s
D) 50 s
Answer: A) 1.5 s
Explanation:
Period = 30 ÷ 20 = 1.5 s.
Q41. Taking repeated readings improves:
A) Mass
B) Accuracy
C) Random error reduction
D) Weight
Answer: C) Random error reduction
Explanation:
Repeating measurements reduces the effect of random variations.
Q42. A digital timer connected to light gates measures:
A) Volume
B) Time automatically
C) Length
D) Force
Answer: B) Time automatically
Explanation:
Light gates trigger timing electronically.
Q43. What is frequency if 40 oscillations take 20 s?
A) 2 Hz
B) 0.5 Hz
C) 20 Hz
D) 40 Hz
Answer: A) 2 Hz
Explanation:
Frequency = Number of oscillations ÷ Time
Frequency = 40 ÷ 20 = 2 Hz
Q44. Why divide total time by number of oscillations?
A) To find frequency
B) To reduce uncertainty
C) To find period
D) To increase speed
Answer: C) To find period
Explanation:
Period = Time for one oscillation.
Q45. Which is NOT a timing instrument?
A) Stop clock
B) Stopwatch
C) Digital timer
D) Measuring cylinder
Answer: D) Measuring cylinder
Explanation:
Measuring cylinder measures volume, not time.
Q46. Which of the following is a scalar quantity?
A) Force
B) Velocity
C) Speed
D) Acceleration
Answer: C) Speed
Explanation:
Speed has magnitude only and no direction. Force, velocity, and acceleration all require direction, so they are vectors.
Q47. Which of the following is a vector quantity?
A) Mass
B) Temperature
C) Weight
D) Time
Answer: C) Weight
Explanation:
Weight is a force and always acts vertically downward, so it has direction and magnitude.
Q48. Which pair consists only of scalar quantities?
A) Speed and velocity
B) Distance and speed
C) Force and acceleration
D) Momentum and displacement
Answer: B) Distance and speed
Explanation:
Distance and speed have magnitude only. Velocity, force, momentum, acceleration, and displacement are vectors.
Q49. Which pair consists only of vector quantities?
A) Force and acceleration
B) Speed and velocity
C) Mass and weight
D) Energy and momentum
Answer: A) Force and acceleration
Explanation:
Both force and acceleration require direction.
Q50. What makes a quantity a vector?
A) It has units
B) It has magnitude
C) It has magnitude and direction
D) It has a large value
Answer: C) It has magnitude and direction
Explanation:
Both magnitude and direction are required for a vector.
Q51. A car travels at 60 km/h north. This describes:
A) Speed
B) Distance
C) Velocity
D) Time
Answer: C) Velocity
Explanation:
Velocity includes direction (north), so it is a vector.
Q52. A student walks 5 m east and then 5 m west. What is the resultant displacement?
A) 10 m
B) 5 m
C) 0 m
D) 2.5 m
Answer: C) 0 m
Explanation:
Displacement is a vector. The movements cancel each other.
Q53. A student walks 5 m east and then 5 m west. What is the total distance travelled?
A) 0 m
B) 5 m
C) 10 m
D) 25 m
Answer: C) 10 m
Explanation:
Distance is scalar and adds normally regardless of direction.
Q54. Which of the following is NOT a vector?
A) Momentum
B) Acceleration
C) Energy
D) Force
Answer: C) Energy
Explanation:
Energy has magnitude only, so it is scalar.
Q55. Weight differs from mass because weight:
A) Is scalar
B) Has no unit
C) Has direction
D) Is constant everywhere
Answer: C) Has direction
Explanation:
Weight is a force acting downward, so it is a vector.
Q56. Which statement about acceleration is correct?
A) It is scalar
B) It has magnitude only
C) It has magnitude and direction
D) It has no units
Answer: C) It has magnitude and direction
Explanation:
Acceleration depends on change in velocity, which includes direction.
Q57. Momentum is a vector because it depends on:
A) Mass only
B) Velocity
C) Speed
D) Energy
Answer: B) Velocity
Explanation:
Momentum = mass × velocity. Since velocity is vector, momentum is vector.
Q58. A force of 10 N east and 10 N west act on an object. What is the resultant force?
A) 20 N east
B) 10 N east
C) 0 N
D) 5 N
Answer: C) 0 N
Explanation:
Vectors in opposite directions cancel.
Q59. Two perpendicular forces of 3 N and 4 N act on an object. What is the resultant force?
A) 7 N
B) 1 N
C) 5 N
D) 12 N
Answer: C) 5 N
Explanation:
Resultant = √(3² + 4²) = √25 = 5 N.
Q60. Which is scalar but often confused with a vector?
A) Velocity
B) Speed
C) Force
D) Acceleration
Answer: B) Speed
Explanation:
Speed does not include direction.
Q61. Which quantity always acts vertically downward near Earth?
A) Mass
B) Weight
C) Speed
D) Energy
Answer: B) Weight
Explanation:
Weight is gravitational force and acts downward.
Q62. Electric field strength is a vector because:
A) It has units
B) It has magnitude only
C) It has magnitude and direction
D) It is large
Answer: C) It has magnitude and direction
Explanation:
Field strength indicates direction of force on positive charge.
Q63. Which quantity is scalar?
A) Displacement
B) Gravitational field strength
C) Time
D) Velocity
Answer: C) Time
Explanation:
Time has magnitude only.
Q64. When adding scalar quantities, we:
A) Use Pythagoras
B) Consider direction
C) Add normally
D) Subtract automatically
Answer: C) Add normally
Explanation:
Scalars do not involve direction.
Q65. When adding vectors in opposite directions, we:
A) Add normally
B) Subtract magnitudes
C) Multiply values
D) Ignore direction
Answer: B) Subtract magnitudes
Explanation:
Opposite directions reduce resultant.
Q66. Which example describes displacement?
A) 100 m
B) 100 m south
C) 100 seconds
D) 100 kg
Answer: B) 100 m south
Explanation:
Displacement requires direction.
Q67. Temperature is scalar because:
A) It has direction
B) It is measured in Kelvin
C) It has magnitude only
D) It changes
Answer: C) It has magnitude only
Q68. If a car moves in a circle at constant speed, its velocity:
A) Is constant
B) Changes direction
C) Is zero
D) Has no magnitude
Answer: B) Changes direction
Explanation:
Velocity is vector. Direction changes continuously in circular motion.
Q69. Which is NOT needed to fully describe a scalar?
A) Magnitude
B) Units
C) Direction
D) Numerical value
Answer: C) Direction
Q70. Which of the following quantities can be zero even if motion occurs?
A) Distance
B) Displacement
C) Speed
D) Time
Answer: B) Displacement
Explanation:
If an object returns to starting point, displacement is zero though distance is not.
Q71. Why are repeated measurements taken in an experiment?
B) To reduce random error
C) To eliminate systematic error completely
D) To make calculations longer
Answer: B) To reduce random error
Explanation: Repeating measurements helps reduce the effect of random fluctuations and improves reliability.
Q72. Which type of error is reduced by averaging readings?
B) Zero error
C) Random error
D) Calibration error
Answer: C) Random error
Explanation: Averaging balances readings that are slightly higher and lower than the true value.
Q73. Three readings are 10 s, 12 s, and 11 s. What is the average?
B) 11 s
C) 12 s
D) 33 s
Answer: B) 11 s
Explanation: Sum = 10 + 12 + 11 = 33; Average = 33 ÷ 3 = 11 s.
Q74. Which of the following may cause random error?
B) Constant zero error
C) Human reaction time
D) Broken scale marking
Answer: C) Human reaction time
Explanation: Reaction time varies and causes unpredictable fluctuations.
Q75. If only one reading is taken, the result may be unreliable because:
B) It may be affected by random error
C) It is too large
D) It is always wrong
Answer: B) It may be affected by random error
Explanation: A single reading may not represent the true value.
B) Sum × Number
C) Sum ÷ Number
D) Measured ÷ Uncertainty
Q77. A student records 5.0 cm, 5.2 cm, and 4.8 cm. What is the average?
A) 5.0 cm
B) 4.8 cm
C) 5.2 cm
D) 15 cm
Answer: A) 5.0 cm
Explanation: Sum = 5.0 + 5.2 + 4.8 = 15.0; Average = 15.0 ÷ 3 = 5.0 cm.
Q78. What is an anomalous result?
A) The highest reading
B) The lowest reading
C) A result very different from others
D) The average value
Answer: C) A result very different from others
Explanation: An anomalous reading does not fit the general pattern.
Q79. If a reading is clearly anomalous, what should be done first?
A) Ignore it immediately
B) Change other readings
C) Check and repeat the measurement
D) Multiply it by 2
Answer: C) Check and repeat the measurement
Explanation: It must be verified before exclusion.
A) Absolute uncertainty
B) Percentage uncertainty
C) Instrument precision
D) Systematic error
Answer: B) Percentage uncertainty
Explanation: Increasing measured value lowers percentage uncertainty.
A) Increases
B) Decreases
C) Stays same
D) Becomes zero
Answer: B) Decreases
Explanation: Percentage uncertainty = (Uncertainty ÷ Measured value) × 100.
Q82. A stopwatch has uncertainty ±0.2 s. A time measured is 2 s. Percentage uncertainty is:
A) 1%
B) 5%
C) 10%
D) 20%
Answer: C) 10%
Explanation: (0.2 ÷ 2) × 100 = 10%.
A) 1%
B) 10%
C) 20%
D) 0.1%
Answer: A) 1%
Explanation: (0.2 ÷ 20) × 100 = 1%.
Q84. Why measure 10 sheets of paper instead of one?
A) To change the ruler
B) To increase uncertainty
C) To reduce percentage error
D) To increase mass
Answer: C) To reduce percentage error
Explanation: Larger total measurement reduces percentage uncertainty.
A) Closeness to true value
B) Consistency of repeated readings
C) Size of value
D) Zero error
Answer: B) Consistency of repeated readings
Explanation: Reliable results are consistent.
A) Consistency
B) Precision
C) Closeness to true value
D) Number of readings
Answer: C) Closeness to true value
Explanation: Accuracy compares measured value to accepted value.
Q87. Which reading set shows poor reliability?
A) 10.0, 10.1, 10.0
B) 10.0, 12.5, 15.0
C) 10.2, 10.1, 10.3
D) 9.9, 10.0, 10.1
Answer: B) 10.0, 12.5, 15.0
Explanation: Large spread indicates poor reliability.
A) Inaccurate
B) Unreliable
C) Reliable
D) Systematic
Answer: C) Reliable
Explanation: Small variation shows consistency.
A) Taking one reading
B) Ignoring units
C) Repeating and averaging
D) Guessing
Answer: C) Repeating and averaging
Explanation: Multiple readings reduce random error.
A) 20 s
B) 2 s
C) 40 s
D) 0.5 s
Answer: B) 2 s
Explanation: Period = 40 ÷ 20 = 2 s.
A) Low uncertainty
B) High precision
C) Large random error
D) Zero error
Answer: C) Large random error
Explanation: Spread indicates random fluctuations.
Q92. Absolute uncertainty refers to:
A) Percentage value
B) Ratio
C) Instrument limit
D) Half smallest division
Answer: D) Half smallest division
Explanation: Uncertainty is usually half the smallest scale division.
A) One precise reading
B) Many repeated readings
C) Ignoring anomalies
D) Estimating
Answer: B) Many repeated readings
Explanation: Repetition improves reliability.
A) It increases reaction time
B) It removes units
C) It reduces percentage uncertainty
D) It changes the instrument
Answer: C) It reduces percentage uncertainty
A) 1%
B) 5%
C) 10%
D) 50%
Answer: C) 10%
Explanation: (0.5 ÷ 5) × 100 = 10%.
A) Time
B) Mass
C) Weight
D) Temperature
Answer: C) Weight
Explanation: Weight is a force acting downward, so it has direction.
A) Its unit
B) Its size
C) Its direction
D) Its symbol
Answer: C) Its direction
Explanation: Vectors require both magnitude and direction.
A) Speed and distance
B) Velocity and force
C) Momentum and acceleration
D) Weight and displacement
Answer: A) Speed and distance
Explanation: Both have magnitude only.
A) Mass and weight
B) Velocity and acceleration
C) Energy and time
D) Speed and momentum
Answer: B) Velocity and acceleration
Explanation: Both include magnitude and direction.
A) Speed
B) Distance
C) Velocity
D) Time
Answer: C) Velocity
Explanation: Direction (east) makes it a vector.
A) 10 N north
B) 2 N north
C) 2 N south
D) 10 N south
Answer: B) 2 N north
Explanation: Subtract magnitudes; direction of larger force remains.
A) 10 m
B) 5 m
C) 0 m
D) 2.5 m
Answer: C) 0 m
Explanation: Displacement depends on change in position.
A) Mass
B) Temperature
C) Distance
D) Force
Answer: D) Force
Explanation: Force has magnitude and direction.
A) Subtraction
B) Multiplication
C) Pythagoras’ theorem
D) Division
Answer: C) Pythagoras’ theorem
A) Mass
B) Distance
C) Velocity
D) Time
Answer: C) Velocity
Explanation: Velocity changes if direction changes.
A) Speed
B) Acceleration
C) Momentum
D) Weight
Answer: A) Speed
A) Upward
B) Horizontal
C) Toward centre of Earth
D) Random
Answer: C) Toward centre of Earth
A) Mass only
B) Velocity
C) Speed
D) Time
Answer: B) Velocity
A) Acceleration
B) Electric field strength
C) Temperature
D) Gravitational field strength
Answer: C) Temperature
A) Consider direction
B) Use Pythagoras
C) Add normally
D) Subtract automatically
Answer: C) Add normally
A) Double
B) Half
C) Zero
D) Same direction
Answer: C) Zero
A) 7 N
B) 5 N
C) 1 N
D) 12 N
Answer: B) 5 N
Explanation: √(3² + 4²) = 5 N.
A) Distance
B) Energy
C) Displacement
D) Temperature
Answer: C) Displacement
A) Distance
B) Speed
C) Velocity
D) Mass
Answer: C) Velocity
A) Acceleration
B) Velocity
C) Time
D) Force
Answer: C) Time
A) Mass
B) Acceleration
C) Temperature
D) Time
Answer: B) Acceleration
Explanation: According to Newton’s Second Law.
A) Has magnitude only
B) Has direction of gravitational force
C) Is constant
D) Is large
Answer: B) Has direction of gravitational force
A) Momentum
B) Speed
C) Weight
D) Displacement
Answer: B) Speed
Q119. If two vectors act in same direction, we:
A) Subtract
B) Multiply
C) Add magnitudes
D) Divide
Answer: C) Add magnitudes
Q120. The arrow in a vector diagram represents:
A) Unit
B) Mass
C) Magnitude and direction
D) Time
Answer: C) Magnitude and direction
Q121. Two forces of 3 N east and 4 N north act on an object. What is the magnitude of the resultant force?
A) 7 N
B) 5 N
C) 1 N
D) 12 N
Answer: B) 5 N
Explanation:
Resultant = √(3² + 4²) = √(9 + 16) = √25 = 5 N.
Q122. The formula used to calculate the resultant of two perpendicular vectors is:
A) A + B
B) A − B
C) √(A² + B²)
D) A × B
Answer: C) √(A² + B²)
Explanation:
This is derived from Pythagoras’ theorem.
Q123. Pythagoras’ theorem can only be used when the vectors are:
A) Parallel
B) Opposite
C) Perpendicular
D) Equal
Answer: C) Perpendicular
Q124. A boat moves 6 m/s east and river flows 8 m/s north. Resultant speed is:
A) 14 m/s
B) 2 m/s
C) 10 m/s
D) 48 m/s
Answer: C) 10 m/s
Explanation:
√(6² + 8²) = √(36 + 64) = √100 = 10 m/s.
Q125. If tan θ = 4/3, the angle θ is approximately:
A) 37°
B) 45°
C) 53°
D) 60°
Answer: C) 53°
Explanation:
tan⁻¹(4/3) ≈ 53°.
Q126. Two perpendicular velocities of 5 m/s and 12 m/s produce a resultant of:
A) 17 m/s
B) 7 m/s
C) 13 m/s
D) 60 m/s
Answer: C) 13 m/s
Explanation:
√(5² + 12²) = √(25 + 144) = √169 = 13 m/s.
Q127. Which trigonometric ratio is used to find direction of resultant?
A) sin θ = opposite ÷ hypotenuse
B) cos θ = adjacent ÷ hypotenuse
C) tan θ = opposite ÷ adjacent
D) tan θ = adjacent ÷ opposite
Answer: C) tan θ = opposite ÷ adjacent
Q128. Two forces of 7 N east and 24 N north act at right angles. Resultant magnitude is:
A) 31 N
B) 17 N
C) 25 N
D) 576 N
Answer: C) 25 N
Explanation:
√(7² + 24²) = √(49 + 576) = √625 = 25 N.
Q129. If two perpendicular vectors are 8 units and 15 units, resultant is:
A) 23
B) 7
C) 17
D) 120
Answer: C) 17
Explanation:
√(8² + 15²) = √(64 + 225) = √289 = 17.
Q130. When finding resultant of perpendicular forces, the final step is:
A) Add values
B) Multiply values
C) Take square root
D) Subtract values
Answer: C) Take square root
Q131. If vectors are not perpendicular, Pythagoras cannot be used because:
A) It gives wrong units
B) It only works for right angles
C) It ignores direction
D) It uses subtraction
Answer: B) It only works for right angles
Q132. Two perpendicular forces of 9 N and 12 N act. Resultant is:
A) 21 N
B) 3 N
C) 15 N
D) 108 N
Answer: C) 15 N
Explanation:
√(9² + 12²) = √(81 + 144) = √225 = 15 N.
Q133. If resultant is 10 N and one component is 6 N, the other perpendicular component is:
A) 4 N
B) 8 N
C) 16 N
D) 100 N
Answer: B) 8 N
Explanation:
10² = 6² + B²
100 = 36 + B²
B² = 64
B = 8 N.
Q134. Two perpendicular velocities produce a resultant of 20 m/s. One component is 12 m/s. The other is:
A) 16 m/s
B) 8 m/s
C) 32 m/s
D) 144 m/s
Answer: A) 16 m/s
Explanation:
20² = 12² + B²
400 = 144 + B²
B² = 256
B = 16 m/s.
Q135. In a vector triangle, the resultant is represented by:
A) The base
B) The height
C) The hypotenuse
D) The angle
Answer: C) The hypotenuse
Q136. If tan θ = 3/4, θ is approximately:
A) 37°
B) 53°
C) 45°
D) 60°
Answer: A) 37°
Explanation:
tan⁻¹(3/4) ≈ 37°.
Q137. Which is required when stating a resultant vector fully?
A) Magnitude only
B) Direction only
C) Magnitude and direction
D) Units only
Answer: C) Magnitude and direction
Q138. Two forces of equal magnitude act at right angles. Resultant is:
A) Double
B) Zero
C) √2 times one force
D) Half
Answer: C) √2 times one force
Explanation:
If both are F:
R = √(F² + F²) = √(2F²) = F√2.
Q139. If a student directly adds 3 N and 4 N to get 7 N for perpendicular forces, this is wrong because:
A) Forces cancel
B) They are scalar
C) Direction is ignored
D) Units wrong
Answer: C) Direction is ignored
Q140. Resultant of two perpendicular vectors depends on:
A) Subtraction only
B) Squaring components
C) Division
D) Multiplication only
Answer: B) Squaring components
Sana Shariq
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