Units and Measurements in Physics
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Questions and Answers

What is the total capacitance when two capacitors with values (1.3 ± 0.1) mF and (2.4 ± 0.2) mF are connected in parallel?

  • (3.7 ± 0.3) mF (correct)
  • (3.6 ± 0.2) mF
  • (3.5 ± 0.1) mF
  • (4.0 ± 0.4) mF

What is the absolute error in the total capacitance when using the individual errors from the two capacitors?

  • ± 0.2 mF
  • ± 0.3 mF (correct)
  • ± 0.1 mF
  • ± 0.4 mF

What is the percentage error in the total capacitance calculated as (3.7 mF)?

  • 7.5%
  • 6.0%
  • 8.1% (correct)
  • 5.0%

Which statement is true regarding percentage error in subtraction compared to addition?

<p>Percentage error is larger in subtraction. (B)</p> Signup and view all the answers

What type of error is represented by the formula ∆Z/Z = ∆A/A + ∆B/B?

<p>Fractional error (A)</p> Signup and view all the answers

What type of error arises from imperfections in experimental technique?

<p>Imperfection Error (D)</p> Signup and view all the answers

Which term describes the difference between the true value and an individual measurement?

<p>Absolute Error (D)</p> Signup and view all the answers

What is the formula for calculating the arithmetic mean of readings?

<p>amean = ∑ ai / n (C)</p> Signup and view all the answers

What type of error is caused by individual bias and improper apparatus settings?

<p>Personal Error (D)</p> Signup and view all the answers

Which of the following best describes random errors?

<p>Errors caused by uncontrolled disturbances (A)</p> Signup and view all the answers

What does the mean absolute error represent?

<p>The average of all absolute errors calculated (B)</p> Signup and view all the answers

In which scenario would parallax error likely occur?

<p>Viewing a scale from an angle (B)</p> Signup and view all the answers

How is probable error related to the number of readings?

<p>It is inversely proportional to the number of readings (A)</p> Signup and view all the answers

What is the SI unit of the gas constant for 1 gram?

<p>Jkg–1 K–1 (C)</p> Signup and view all the answers

Which of the following is the dimensional formula for the gas constant?

<p>[M0 L2 T–2 q–1] (D)</p> Signup and view all the answers

The Boltzmann constant is associated with which of the following units?

<p>JK–1 molecule–1 (B)</p> Signup and view all the answers

What does the formula for mechanical equivalent of heat indicate?

<p>[M0 L0 T0] (D)</p> Signup and view all the answers

Which physical quantity has the formula dQ/dt?

<p>Thermal conductivity (D)</p> Signup and view all the answers

What is the dimensional formula for entropy?

<p>[M1 L2 T–2 q–1] (B)</p> Signup and view all the answers

Which of the following represents the coefficient of thermal conductivity?

<p>Js–1 m–1 K–1 (B)</p> Signup and view all the answers

Which physical quantity is defined as the ratio of heat energy to temperature?

<p>Entropy (B)</p> Signup and view all the answers

What is the term used to describe the smallest division that can be measured accurately with a screw gauge?

<p>Least Count (B)</p> Signup and view all the answers

If the zero of the vernier scale lies ahead of the Nth division of the main scale, which reading is the main scale reading represented by?

<p>N (A)</p> Signup and view all the answers

What happens when the nth division of the vernier scale coincides with any division of the main scale?

<p>It gives the Vernier Scale Reading. (A)</p> Signup and view all the answers

To find the total reading (T.R.) with a screw gauge, which components are required?

<p>M.S.R., V.S.R., and n rotations (D)</p> Signup and view all the answers

In the context of the screw gauge, what does 'n' represent?

<p>The number of rotations of the screw (A)</p> Signup and view all the answers

What is the purpose of rotating the screw gauge during measurement?

<p>To bring zero of the circular scale on the reference line (C)</p> Signup and view all the answers

How is the distance moved by the screw determined in relation to the number of rotations?

<p>Distance = n × (Least Count) (D)</p> Signup and view all the answers

What does T.R. = M.S.R. + V.S.R. indicate?

<p>It describes the total reading of the screw gauge. (A)</p> Signup and view all the answers

What is the least count of the instrument defined in the content?

<p>0.020 cm (C)</p> Signup and view all the answers

How many divisions does the main scale of the vernier caliper consist of?

<p>200 (A)</p> Signup and view all the answers

What is the total distance traveled in four complete revolutions of the screw gauge, as per the content?

<p>2 mm (A)</p> Signup and view all the answers

What can be calculated using the formula for pitch in the content?

<p>Linear distance in one revolution (C)</p> Signup and view all the answers

What is the value of one division on the main scale of the vernier caliper if it's divided into 200 divisions?

<p>0.05 cm (C)</p> Signup and view all the answers

How many divisions are there on the circular scale of the screw gauge mentioned in the content?

<p>50 (C)</p> Signup and view all the answers

What is the formula for calculating the pitch of the screw gauge?

<p>Length traveled in one revolution (D)</p> Signup and view all the answers

If the least count of the instrument is 0.001 cm, which of the following would be correct?

<p>Smaller than the existing least count (C)</p> Signup and view all the answers

What is the dimensional status of the equation St = U + a(2t - 1)?

<p>Neither numerically nor dimensionally correct (B)</p> Signup and view all the answers

What is the mass density value given in the content?

<p>1.12 × 10^3 kg/m^3 (C)</p> Signup and view all the answers

What are the dimensions of resistance in an electrical circuit?

<p>[ML^2T^-1I^-1] (C)</p> Signup and view all the answers

What can be inferred from the value Δm = 1 gm?

<p>It is equal to 0.001 kg (A)</p> Signup and view all the answers

What is the numerical error calculated for the density Δρ?

<p>3.59 kg/m^3 (C)</p> Signup and view all the answers

Which physical quantity does Planck's constant dimensionally equate to?

<p>Angular momentum (D)</p> Signup and view all the answers

What is the equivalent expression for the pressure change in the content ΔP?

<p>Δρ = (0.001/4.692) / (10.01) (D)</p> Signup and view all the answers

In the expression for distance traveled, what does U represent?

<p>Velocity (C)</p> Signup and view all the answers

Flashcards

Universal Gas Constant

The universal gas constant, denoted by R, relates the pressure, volume, temperature, and amount of a gas in the ideal gas law. It's a proportionality constant.

Gas Constant (for 1 gram)

The gas constant for one gram of a substance relates the amount of heat involved in a temperature change.

Boltzmann Constant

The Boltzmann constant, k, is a fundamental constant that relates the average kinetic energy of a particle in a gas to the temperature of the gas. It connects microscopic gas behavior to macroscopic temperature scales.

Mechanical equivalent of heat

The mechanical equivalent of heat, J, is a constant that relates mechanical work to heat energy. It represents the work required to produce a unit of heat.

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Coefficient of Thermal Conductivity

The coefficient of thermal conductivity, K, describes how easily a material transmits heat energy.

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Entropy

Entropy, often denoted as dQ/T, is the measure of disorder or randomness in a thermodynamic system. It relates the change in heat energy to temperature.

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Specific Heat

Specific Heat is the amount of heat required to raise the temperature of one gram of a substance by 1 degree Celsius.

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True Value

The arithmetic mean of multiple readings that are very close to the most accurate measurement.

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Imperfection Error

Errors due to experimental setup, procedures, and techniques.

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Personal Error

Errors caused by individual biases, apparatus setup issues, or carelessness in observation.

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Absolute Error

The difference between the true value and an individual measurement.

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Mean Absolute Error

The average of all absolute errors.

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Random Error

Errors caused by uncontrolled disturbances impacting the measurement.

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Measuring Instrument Error

Error in measurement due to limitations of the measuring instrument or by applying improper corrections.

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Least Count of Screw Gauge

The smallest measurable increment of length in a screw gauge. It's calculated by dividing the pitch of the screw by the number of divisions on the circular scale.

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Pitch of a Screw

The distance the screw advances along its axis for one complete rotation.

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Main Scale Reading (MSR)

The reading on the linear scale of the instrument (screw gauge).

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Vernier Scale Reading (VSR)

The reading on the vernier scale of the instrument, corresponding to the fraction of the smallest division on the main scale.

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Total Reading (TR)

The sum of the main scale reading and the vernier scale reading.

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Screw Gauge Zero Error

The error when the zero of the circular scale doesn't coincide with the reference line on the linear scale.

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Parallel Capacitors

When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances.

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Total Capacity

The overall capacitance of a combination of capacitors.

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Absolute Error

The magnitude of the error in a measurement.

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Percentage Error

The error expressed as a percentage of the measured value.

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Relative Error

The error in a measurement relative to the measured value.

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Significant Figures

The number of reliable digits in a measured or calculated value.

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Fractional Error

Another term for Relative Error.

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Error in Addition/Subtraction

The absolute errors add up in addition/subtraction whereas the relative errors add up in multiplication/division.

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Error in Multiplication/Division

The relative errors add up in multiplication/division.

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Least Count (Vernier Caliper)

The smallest measurement that can be accurately determined using a vernier caliper.

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Main Scale Divisions (Vernier Caliper)

The larger divisions on the vernier caliper's main scale.

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Vernier Scale Divisions

The smaller divisions on the vernier caliper's vernier scale.

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Least Count of Screw Gauge

Smallest change in the measurement that the instrument can detect .

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Pitch of a screw gauge

The distance moved by the spindle for one complete rotation.

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Circular Scale Divisions (Screw Gauge)

Number of divisions present on the circular scale of the screw gauge.

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Dimensional correctness of equation

An equation is dimensionally correct if the dimensions of all terms on both sides of the equation are the same.

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Numerical correctness of equation

An equation is numerically correct if the calculated value from the equation matches the expected value.

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Planck's Constant Dimension

Planck's constant has the same dimensions as angular momentum.

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Resistance Dimension

Resistance in an electrical circuit has dimensions of [ML^2T^-3I^-2].

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Error in Density Calculation

The error in calculating density depends on the errors in mass and volume measurements.

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Study Notes

Units and Measurements

  • Universal gas constant (R): J mol⁻¹ K⁻¹
  • Gas constant for 1 gram (r): J kg⁻¹ K⁻¹
  • Boltzmann constant (k): J K⁻¹ molecule⁻¹
  • Mechanical equivalent of heat (J): No S.I. units
  • Coefficient of thermal conductivity (K): W m⁻¹ K⁻¹
  • Entropy: J K⁻¹
  • Dimensional formula for resistance: [ML²T⁻³I⁻²]

Error Analysis

  • True value: Arithmetic mean of all readings, closest to most accurate reading
  • Absolute error (Δai): Magnitude of difference between true value and individual measurement
  • Mean absolute error: Arithmetic mean of all absolute errors
  • Random errors: Uncontrolled disturbances influencing physical quantity or instrument, estimated statistically.
  • Imperfection errors: Errors due to experimental arrangement, procedure, or technique. Examples include heat loss in calorimetry, air buoyancy effects in weighing.
  • Personal errors: Errors due to individual bias, improper apparatus settings, or carelessness in observation. Examples include parallax errors.
  • Relative error: Fractional error, calculated as ΔZ/Z.
  • Percentage error: Relative error multiplied by 100%.
  • Error propagation in addition/subtraction: Absolute error in result is sum of individual absolute errors, and percentage error in result increases

Significant Figures

  • Significant figures: Figures considered trustworthy in a number. Example: 3.141592654 (up to 10 digits)

Screw Gauge/Spherometer

  • Least count (L.C.): Pitch/Total divisions on circular scale.
  • Pitch: Linear distance moved by screw for one complete rotation.
  • Main scale reading (M.S.R.): Number of main scale divisions the zero of vernier scale lies past.
  • Vernier scale reading (V.S.R.): Number of vernier scale divisions coinciding with main scale divisions.
  • Total reading (T.R.): M.S.R. + V.S.R.

Example Calculations

  • Parallel Capacitors: If C₁ = (1.3 ± 0.1) mF and C₂ = (2.4 ± 0.2) mF, then Cp = (3.7 ± 0.3) mF; % error = 8.1%
  • Screw Gauge: If 1 main scale div = 0.1 cm, 10 vernier divisions = 8 main scale divisions, L.C. = 0.02 cm
  • Pitch of Screw Gauge: If 4 full rotations result in a distance of 2 mm on the pitch scale, pitch = 0.5 mm = 0.05 cm
  • Least Count of Screw Gauge: If there are 50 divisions on the circular scale, Least Count (L.C.) = pitch / 50

Dimensional Analysis

  • Planck's constant: has dimensions of energy × time.

Formulas, not specifically explained

  • Derivation for finding Least Count of a Screw Gauge: 1 Main scale division = $0.05 cm$, 10 Vernier Divisions = 8 main scale divisions, Least Count of Vernier Caliper = 0.002 cm
  • ∆Z = √(∆A² + ∆B²) in multiplication or division

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Description

This quiz focuses on the essential units and measurements in physics, including the universal gas constant, Boltzmann constant, and thermal conductivity. It also covers error analysis, discussing concepts such as absolute error and random errors. Test your knowledge on these fundamental principles of physics!

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