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.</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</p> Signup and view all the answers

    What type of error arises from imperfections in experimental technique?

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

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

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

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

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

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

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

    Which of the following best describes random errors?

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

    What does the mean absolute error represent?

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

    In which scenario would parallax error likely occur?

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

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

    <p>Jkg–1 K–1</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]</p> Signup and view all the answers

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

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

    What does the formula for mechanical equivalent of heat indicate?

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

    Which physical quantity has the formula dQ/dt?

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

    What is the dimensional formula for entropy?

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

    Which of the following represents the coefficient of thermal conductivity?

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

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

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

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

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

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

    <p>200</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</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</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</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</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</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</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</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</p> Signup and view all the answers

    What are the dimensions of resistance in an electrical circuit?

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

    What is the numerical error calculated for the density Δρ?

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

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

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

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

    <p>Velocity</p> Signup and view all the answers

    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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