Tuesday, 23 September 2025

Chapter 1: Units & Measurements - Basic Quiz

September 23, 2025 0

Chapter 1: Units & Measurements - Basic Quiz (50 Questions)

Chapter 1: Units & Measurements – MCQ Quiz

Q1. Which of the following is a fundamental quantity?

A) Speed

B) Force

C) Length

D) Pressure

✅ Correct Answer: C) Length

🔍 Explanation: Length is one of the seven SI base quantities; speed, force, and pressure are derived.

Q2. The SI base unit of mass is:

A) gram

B) kilogram

C) pound

D) tonne

✅ Correct Answer: B) kilogram

🔍 Explanation: Kilogram (kg) is the SI base unit of mass; gram is its submultiple.

Q3. Which of these is NOT an SI base quantity?

A) Time

B) Electric current

C) Luminous intensity

D) Pressure

✅ Correct Answer: D) Pressure

🔍 Explanation: Pressure is a derived quantity (force per unit area), not a base SI quantity.

Q4. The SI unit of temperature is:

A) Celsius

B) Kelvin

C) Fahrenheit

D) Joule

✅ Correct Answer: B) Kelvin

🔍 Explanation: Kelvin (K) is the SI base unit of thermodynamic temperature.

Q5. A steradian measures:

A) Plane angle

B) Solid angle

C) Area

D) Volume

✅ Correct Answer: B) Solid angle

🔍 Explanation: Steradian (sr) is the SI derived unit of solid angle.

Q6. The dimensional formula of force is:

A) [M L T⁻²]

B) [M L² T⁻²]

C) [M L T⁻¹]

D) [L T⁻²]

✅ Correct Answer: A) [M L T⁻²]

🔍 Explanation: Force = mass × acceleration ⇒ [M] [L T⁻²].

Q7. Which prefix multiplies a unit by 10⁻³?

A) micro-

B) milli-

C) centi-

D) kilo-

✅ Correct Answer: B) milli-

🔍 Explanation: “Milli” denotes 10⁻³; “micro” denotes 10⁻⁶.

Q8. The least count error is an example of:

A) Random error

B) Systematic error

C) Parallax error

D) Human error

✅ Correct Answer: B) Systematic error

🔍 Explanation: Least‐count error biases every measurement by a constant amount.

Q9. Parallax error arises when:

A) Zero is mis‐set

B) Observer’s eye is misaligned

C) Instrument vibrates

D) Scale is non‐uniform

✅ Correct Answer: B) Observer’s eye is misaligned

🔍 Explanation: Viewing the scale from an angle shifts the apparent mark.

Q10. A vernier caliper typically has least count:

A) 0.1 cm

B) 0.01 cm

C) 1 mm

D) 0.5 mm

✅ Correct Answer: B) 0.01 cm

🔍 Explanation: Standard vernier calipers read to 0.01 cm (0.1 mm).

Q11. A screw gauge’s least count is usually:

A) 0.1 mm

B) 0.01 mm

C) 0.001 mm

D) 0.05 mm

✅ Correct Answer: B) 0.01 mm

🔍 Explanation: Screw gauges typically measure down to 0.01 mm.

Q12. How many significant figures are in 0.00450?

A) 2

B) 3

C) 4

D) 5

✅ Correct Answer: B) 3

🔍 Explanation: Significant figures are 4, 5 and the zero between them counts; leading zeros do not.

Q13. Which of these is dimensionless?

A) Force

B) Solid angle

C) Density

D) Work

✅ Correct Answer: B) Solid angle

🔍 Explanation: Solid angle in steradians is a ratio of areas, so it is dimensionless.

Q14. The formula for density is:

A) ρ = V/m

B) ρ = m/V

C) ρ = m·V

D) ρ = m + V

✅ Correct Answer: B) ρ = m/V

🔍 Explanation: Density equals mass divided by volume.

Q15. Percentage error is defined as:

A) (x – Δx)/x × 100

B) (Δx/x) × 100

C) (Δx – x) × 100

D) (x/Δx) – 100

✅ Correct Answer: B) (Δx/x) × 100

🔍 Explanation: Percentage error = (absolute error ÷ true value) × 100.

Q16. The dimensional formula of energy is:

A) [M L T⁻²]

B) [M L² T⁻²]

C) [M L² T⁻³]

D) [M L⁻³ T⁰]

✅ Correct Answer: B) [M L² T⁻²]

🔍 Explanation: Energy has dimensions of mass·(length)²/(time)².

Q17. Which derived unit is equivalent to N·m?

A) Joule

B) Watt

C) Pascal

D) Newton

✅ Correct Answer: A) Joule

🔍 Explanation: Work or energy in SI is measured in joules (N·m).

Q18. Power has dimensions:

A) [M L² T⁻³]

B) [M L² T⁻²]

C) [M L T⁻²]

D) [L T⁻¹]

✅ Correct Answer: A) [M L² T⁻³]

🔍 Explanation: Power = energy/time ⇒ [ML²T⁻²]/[T] = [ML²T⁻³].

Q19. Total solid angle around a point is:

A) 2π sr

B) 4π sr

C) π sr

D) 360°

✅ Correct Answer: B) 4π sr

🔍 Explanation: A full sphere subtends 4π steradians.

Q20. For a small plane angle dθ:

A) dθ = r/ds

B) dθ = ds/r

C) dθ = ds·r

D) dθ = ds + r

✅ Correct Answer: B) dθ = ds/r

🔍 Explanation: dθ equals arc length divided by radius.

Q21. For a small solid angle dΩ:

A) dΩ = dA·r²

B) dΩ = dA/r²

C) dΩ = r²/dA

D) dΩ = dA + r²

✅ Correct Answer: B) dΩ = dA/r²

🔍 Explanation: Solid angle = area on sphere divided by square of radius.

Q22. Which of these is an SI derived unit?

A) Metre

B) Candela

C) Mole

D) Newton

✅ Correct Answer: D) Newton

🔍 Explanation: Newton is derived: kg·m/s².

Q23. The SI base unit of amount of substance is:

A) Mole

B) Candela

C) Ampere

D) Kelvin

✅ Correct Answer: A) Mole

🔍 Explanation: Mole (mol) is the SI base unit for amount of substance.

Q24. The SI unit of luminous intensity is:

A) Lux

B) Lumen

C) Candela

D) Watt

✅ Correct Answer: C) Candela

🔍 Explanation: Candela (cd) is the SI base unit of luminous intensity.

Q25. The dimensional formula [M⁰ L⁰ T⁰] denotes:

A) Force

B) Velocity

C) Dimensionless quantity

D) Energy

✅ Correct Answer: C) Dimensionless quantity

🔍 Explanation: Dimensionless quantities have no M, L, or T factors.

Q26. Which instrument measures very small lengths accurately?

A) Meter scale

B) Vernier caliper

C) Screw gauge

D) Stopwatch

✅ Correct Answer: C) Screw gauge

🔍 Explanation: Screw gauges measure small dimensions to 0.01 mm.

Q27. A measurement 12.30 ± 0.05 has a precision of:

A) 0.05 units

B) 0.5 units

C) 0.005 units

D) 0.1 units

✅ Correct Answer: A) 0.05 units

🔍 Explanation: Precision equals the absolute error value.

Q28. Systematic errors can be reduced by:

A) Taking multiple readings

B) Calibration

C) Random trials

D) Averaging

✅ Correct Answer: B) Calibration

🔍 Explanation: Calibration corrects consistent instrument bias.

Q29. Random errors are minimized by:

A) Calibration

B) Repeated measurements and averaging

C) Zero‐setting

D) Correct eye alignment

✅ Correct Answer: B) Repeated measurements and averaging

🔍 Explanation: Averaging multiple trials reduces random fluctuations.

Q30. The SI prefix “giga-” means:

A) 10⁶

B) 10⁹

C) 10⁻⁶

D) 10⁻⁹

✅ Correct Answer: B) 10⁹

🔍 Explanation: “Giga” denotes 10⁹.

Q31. Convert 90 km/h to m/s:

A) 25 m/s

B) 30 m/s

C) 22.5 m/s

D) 15 m/s

✅ Correct Answer: A) 25 m/s

🔍 Explanation: Multiply by 5/18: 90×5/18 = 25 m/s.

Q32. The unit Pascal (Pa) equals:

A) N/m

B) N/m²

C) J/m³

D) W/m²

✅ Correct Answer: B) N/m²

🔍 Explanation: 1 Pa = 1 N per square metre.

Q33. Which has the same dimensions as work?

A) Energy

B) Pressure

C) Power

D) Force

✅ Correct Answer: A) Energy

🔍 Explanation: Work and energy share dimensions [M L² T⁻²].

Q34. The equation x = x₀ + v₀t + ½at² applies when:

A) Acceleration is variable

B) Acceleration is constant

C) Velocity is zero

D) Displacement is zero

✅ Correct Answer: B) Acceleration is constant

🔍 Explanation: That kinematic formula holds for uniform acceleration.

Q35. A reading 3.060 g has how many significant figures?

A) 2

B) 3

C) 4

D) 5

✅ Correct Answer: C) 4

🔍 Explanation: All nonzero and captive zeros count: 3, 0, 6, 0.

Q36. Which cancels systematic zero error?

A) Flip the instrument and average

B) Align your eye properly

C) Change scale

D) Use a different instrument

✅ Correct Answer: A) Flip the instrument and average

🔍 Explanation: Averaging direct and reversed readings cancels zero shift.

Q37. The product error formula Δ(AB) = AB(ΔA/A + ΔB/B) holds when:

A) A and B are added

B) A and B are multiplied

C) A and B are divided

D) A and B are subtracted

✅ Correct Answer: B) A and B are multiplied

🔍 Explanation: Relative errors add for a product.

Q38. Which quantity has dimensions [M⁰ L T⁻¹]?

A) Velocity

B) Acceleration

C) Force

D) Frequency

✅ Correct Answer: A) Velocity

🔍 Explanation: Velocity = distance/time ⇒ [L T⁻¹].

Q39. Frequency’s dimensional formula is:

A) [T]

B) [T⁻¹]

C) [L T⁻¹]

D) [M L⁻¹ T⁻²]

✅ Correct Answer: B) [T⁻¹]

🔍 Explanation: Frequency is cycles per second ⇒ 1/time.

Q40. A quantity √(distance³/time) has dimensions:

A) [L³ T⁻¹]½

B) [L³ T]½

C) [L³ T⁻²]½

D) [L T⁻¾]

✅ Correct Answer: A) [L³ T⁻¹]½

🔍 Explanation: Under the square root: (length³/time) gives [L³ T⁻¹]; then take ½ power.

Q41. To convert cm³ to m³ multiply by:

A) 10⁻³

B) 10⁻⁶

C) 10⁻⁹

D) 10³

✅ Correct Answer: B) 10⁻⁶

🔍 Explanation: (10⁻²)³ = 10⁻⁶.

Q42. The symbol ρ in ρ = m/V stands for:

A) Resistivity

B) Permittivity

C) Density

D) Pressure

✅ Correct Answer: C) Density

🔍 Explanation: ρ is the symbol for density in physics.

Q43. The SI unit of electric potential difference is:

A) Volt

B) Coulomb

C) Ohm

D) Ampere

✅ Correct Answer: A) Volt

🔍 Explanation: Potential difference in SI is measured in volts (V).

Q44. The unit of charge, coulomb, equals:

A) A·s

B) V·s

C) C·V

D) N·m

✅ Correct Answer: A) A·s

🔍 Explanation: 1 C = 1 ampere × 1 second.

Q45. A measurement 0.670 L has how many significant figures?

A) 2

B) 3

C) 4

D) 1

✅ Correct Answer: B) 3

🔍 Explanation: Nonzero and captive zeros count: 0.670 has three significant figures.

Q46. Which of these is NOT an SI unit?

A) Metre

B) Kilogram

C) Litre

D) Second

✅ Correct Answer: C) Litre

🔍 Explanation: Litre is a non‐SI unit of volume (1 L = 10⁻³ m³).

Q47. The dimensions of kinematic viscosity ν = μ/ρ are:

A) [L² T⁻¹]

B) [L T⁻¹]

C) [M L⁻³ T⁻¹]

D) [M L T⁻²]

✅ Correct Answer: A) [L² T⁻¹]

🔍 Explanation: Kinematic viscosity = dynamic viscosity/density ⇒ [L²/T].

Q48. Which of these is a base-10 submultiple?

A) kilo-

B) deci-

C) mega-

D) giga-

✅ Correct Answer: B) deci-

🔍 Explanation: “Deci” denotes 10⁻¹, a submultiple of one.

Q49. The unit of illumination (lux) is:

A) lumen/m²

B) candela/m²

C) watt/m²

D) lumen·m²

✅ Correct Answer: A) lumen/m²

🔍 Explanation: Lux = lumens per square metre.

Q50. The method of least squares is employed to:

A) Reduce systematic error

B) Minimize random error in a fit

C) Calibrate zero

D) Increase precision

✅ Correct Answer: B) Minimize random error in a fit

🔍 Explanation: Least squares finds the best-fit line by minimizing the sum of squared deviations of the data points from the fitted curve.

Sunday, 21 September 2025

UNIT 1: Units and Measurements - Key Formulas

September 21, 2025 0

Units and Measurements - Key Formulas

1. Plane Angle

Formula: $d θ = \frac{d s}{r}$

What each symbol stands for:

$d θ$ : infinitesimal plane angle
$d s$ : infinitesimal arc length
$r$ : radius of the circle

Example A circle of radius $r=2.0$ m has an arc length $d s = 1.0$ m.

d θ = \frac{1.0}{2.0} = 0.50 rad

2. Solid Angle

Formula

d Ω = \frac{d A}{r^{2}}

What each symbol stands for

$d Ω$ : infinitesimal solid angle
$d A$ : small patch of area on a spherical surface
$r$ : radius of the sphere

Simple example On a sphere of radius $r=1.0$ m, a tiny patch has $dA=0.20$ m².

d Ω = \frac{0.20}{{1.0}^{2}} = 0.20 (steradian)

3. Density

Formula

ρ = \frac{m}{V}

What each symbol stands for

$ρ$ : mass density of the material
$m$ : mass of the object
$V$ volume occupied by the object

Simple example A metal block has mass $m=12.0$ g and volume $V=3.0$ cm³.

ρ = \frac{12.0}{3.0} = 4.0 (g/cm³)

4. Newton’s Second Law (Force)

Formula

F = m a

What each symbol stands for

$F$ : net force acting on an object
$m$ : mass of the object
$a$ : acceleration of the object

Simple example A cart of mass $m=2.0$ kg accelerates at $a=3.0$ m/s².

F = 2.0 \times 3.0 = 6.0 (N)

5. Kinematic Equation (Constant Acceleration)

Formula

x = x_{0} + v_{0} t + \frac{1}{2} a t^{2}

What each symbol stands for

$x$ : displacement after time $t$
$x_{0}$ : initial displacement (at $t = 0$ )
$v_{0}$ : initial velocity (at $t = 0$ )
$t$ : elapsed time
$a$ : constant acceleration

Simple example Start from $x_{0} = 0$ , with $v_{0} = 2.0$ m/s and $a a=1.0$ m/s². After $t=3.0$ s:

x = 0 + (2.0) (3.0) + \frac{1}{2} (1.0) (3.0)^{2} = 6.0 + 4.5 = 10.5 m

6. Period of a Simple Pendulum

Formula

T = 2 π \sqrt{\frac{l}{g}}

What each symbol stands for

$T$ : time period of one complete oscillation
$π$ : mathematical constant (≈ 3.1416)
$l$ : length of the pendulum
$g$ : acceleration due to gravity

Simple example A pendulum of length $l=1.0$ m on Earth ( $g=9.8$ m/s²):

T = 2 π \sqrt{\frac{1.0}{9.8}} \approx 2.01 s

7. Percentage (Relative) Error

Formula

% error = \frac{Δ x}{x} \times 100

What each symbol stands for

$% error$ : percentage uncertainty in the measurement
$Δ x$ : absolute error in the measured quantity
$x$ : measured value

Simple example A length $x=50.0$ cm has an uncertainty $Δ x = 0.5$ cm.

% error = \frac{0.5}{50.0} \times 100 = 1.0 %

8. Error in a Product

Formula

Δ (A B) = A B (\frac{Δ A}{A} + \frac{Δ B}{B})

What each symbol stands for

$Δ (A B)$ : absolute error in the product $A \times B$
$A, B$ : measured quantities being multiplied
$Δ A, Δ B \$ : absolute errors in $A$ and $B$

Simple example $A = 4.0 \pm 0.1$ , $B = 2.0 \pm 0.2$ :

Product: $4.0\times2.0=8.0$
Relative errors: $\frac{0.1}{4.0} = 0.025, \frac{0.2}{2.0} = 0.10$
Sum of rel. errors: $0.025 + 0.10 = 0.125$
Absolute error: $Δ (A B) = 8.0 \times 0.125 = 1.0$

A B = 8.0 \pm 1.0

Thursday, 15 May 2025

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Tuesday, 23 September 2025

Chapter 1: Units & Measurements - Basic Quiz

Chapter 1: Units & Measurements – MCQ Quiz

Sunday, 21 September 2025

UNIT 1: Units and Measurements - Key Formulas

Units and Measurements - Key Formulas

1. Plane Angle

2. Solid Angle

3. Density

4. Newton’s Second Law (Force)

5. Kinematic Equation (Constant Acceleration)

6. Period of a Simple Pendulum

7. Percentage (Relative) Error

8. Error in a Product

Thursday, 15 May 2025

11

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