Podcast
Questions and Answers
Given that force is the product of mass and acceleration, and that the S.I. unit of mass is a base unit, why is the S.I. unit of force considered a derived unit?
Given that force is the product of mass and acceleration, and that the S.I. unit of mass is a base unit, why is the S.I. unit of force considered a derived unit?
- Because force is only relevant in specific scenarios, such as gravitational fields.
- Because force can be expressed in terms of base units of mass, length, and time. (correct)
- Because force is a fundamental property and requires no other units to define it.
- Because the unit of force depends on the value of gravitational acceleration.
If power is defined as work done per unit time, and work is force times distance, which of the following correctly represents the dimensional formula of power?
If power is defined as work done per unit time, and work is force times distance, which of the following correctly represents the dimensional formula of power?
- $[M^{2}L^{2}T^{-3}]$
- $[MLT^{-2}]$
- $[ML^{2}T^{-3}]$ (correct)
- $[ML^{2}T^{-2}]$
A student claims a screw gauge is more precise than a vernier caliper because it can measure smaller lengths. How does the least count relate to this increased precision?
A student claims a screw gauge is more precise than a vernier caliper because it can measure smaller lengths. How does the least count relate to this increased precision?
- The least count has no relation to the precision of the instrument.
- A smaller least count means the instrument can measure smaller differences in length. (correct)
- A larger least count allows for more estimations between scale divisions.
- The least count determines the maximum length that can be measured.
The Vernier constant is essential for precise measurements using a Vernier caliper. How is the Vernier constant defined and what does it determine?
The Vernier constant is essential for precise measurements using a Vernier caliper. How is the Vernier constant defined and what does it determine?
A student measures a length and records it as 2.500 cm. How many significant figures are in this measurement and what does it imply about the precision?
A student measures a length and records it as 2.500 cm. How many significant figures are in this measurement and what does it imply about the precision?
Consider the equation $s = ut + \frac{1}{2}at^2$. If the dimensions of displacement (s) are [L], initial velocity (u) is [LT⁻¹], time (t) is [T], and acceleration (a) is [LT⁻²], what does the dimensional correctness of this equation imply?
Consider the equation $s = ut + \frac{1}{2}at^2$. If the dimensions of displacement (s) are [L], initial velocity (u) is [LT⁻¹], time (t) is [T], and acceleration (a) is [LT⁻²], what does the dimensional correctness of this equation imply?
Why is the Angstrom unit particularly useful in fields like spectroscopy and atomic physics, even though it is not an SI unit?
Why is the Angstrom unit particularly useful in fields like spectroscopy and atomic physics, even though it is not an SI unit?
A student takes multiple readings of a voltage to minimize errors. Which type of error is primarily being addressed by this method, and how does averaging help?
A student takes multiple readings of a voltage to minimize errors. Which type of error is primarily being addressed by this method, and how does averaging help?
An engineer derives an equation for fluid flow but realizes it is dimensionally inconsistent. What can be concluded about the validity of this equation?
An engineer derives an equation for fluid flow but realizes it is dimensionally inconsistent. What can be concluded about the validity of this equation?
Given the equation $v = u + at$, a student claims that all terms must have the dimensions of length [L]. Is this statement correct, and why?
Given the equation $v = u + at$, a student claims that all terms must have the dimensions of length [L]. Is this statement correct, and why?
Flashcards
Derived Unit
Derived Unit
SI unit of force is derived from base units.
Power's Dimension
Power's Dimension
The dimensional formula for power is [ML²T⁻³].
Screw Gauge Precision
Screw Gauge Precision
Screw gauges have smaller least counts than vernier calipers, allowing more precise measurements.
Vernier Constant
Vernier Constant
The difference between one main scale division and one vernier scale division.
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Significant Zeros
Significant Zeros
Trailing zeros after a decimal point are significant.
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Dimensional Consistency
Dimensional Consistency
An equation must have consistent dimensions to be valid
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Angstrom Unit
Angstrom Unit
Angstrom is 10⁻¹⁰ meters; used for light wavelengths.
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Reducing Random Errors
Reducing Random Errors
Averaging multiple readings minimizes random errors.
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Correctness and Dimensions
Correctness and Dimensions
Valid equations are dimensionally consistent.
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Limitations of Dimension
Limitations of Dimension
Dimensional analysis cannot deduce numerical constants.
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Units and Measurements
- The S.I. unit of force is a derived unit.
- Force is defined as the product of mass and acceleration.
- The dimensional formula of power is [ML²T⁻³].
- Power is defined as work done per unit time.
- A screw gauge can measure smaller lengths than a vernier caliper.
- A screw gauge has a smaller least count than a vernier caliper.
- A Vernier constant is the difference between one main scale division and one vernier scale division.
- The Vernier constant determines the least count of a vernier caliper.
- The number 2.500 has 4 significant figures.
- Trailing zeros are not counted in significant figures if there is a decimal point.
- The equation s= ut + (1/2)at² is dimensionally correct.
- The dimensions of all terms in an equation must be the same for it to be valid.
- 1 Angstrom = 10⁻¹⁰ cm.
- Angstrom is commonly used to express the wavelength of light and atomic radii.
- Random errors can be minimized by taking multiple readings and calculating the average.
- Systematic errors cannot be reduced by taking multiple readings.
- An equation is valid only if it is dimensionally consistent.
- Dimensional analysis does not ensure the correctness of equations in all cases.
- The equation v = u + at is dimensionally homogeneous.
- All terms in the equation have the same dimensions.
- Dimensional analysis can determine the correctness of a derived equation.
- Dimensional analysis also helps in converting units between different measurement systems.
- The equation v² = u² + 2as is incorrect dimensionally.
- The dimensions of v² and u² are the same as that of 2as.
- Dimensional analysis cannot determine proportionality constants in physical equations.
- Dimensionally consistent equations may still be incorrect due to missing numerical factors.
- Displacement gradient is a dimensionless quantity.
- Displacement is not a dimensionless quantity.
- A unitless physical quantity may or may not be dimensionless.
- A pure number is always dimensionless.
- All physically correct equations are dimensionally correct.
- All dimensionally correct equations are not physically correct.
- When the unit for the measurement of a physical quantity changes, its numerical value changes.
- The product of numerical value of the physical quantity and unit for a quantity remains constant.
- Physical relations involving addition and subtraction cannot be derived by dimensional analysis.
- Numerical constants cannot be deduced by the method of dimensions.
- A dimensionless quantity may have a unit.
- Two physical quantities having the same dimensions, may have different S.I. units.
- The formula K = (1/2)mv² + ma is dimensionally incorrect.
- Physical quantities of different dimensions cannot be added or subtracted.
- Kinetic energy has the dimensional formula [ML²T⁻²].
- Dimensional analysis can determine physical constants like k in T = k√(l/g).
- Dimensions of LHS and RHS must match for an equation to be dimensionally consistent.
- In a Vernier calipers, one vernier scale division is always smaller than one main scale division.
- The Vernier constant is given by one main scale division divided by the number of vernier scale divisions.
- The dimensional formula of electric resistance is [ML²T⁻³I⁻²].
- The dimensional formula of the coefficient of thermal conductivity is [MLT⁻³K⁻¹].
- The result of the area of a square having a side of 0.50 cm will contain 2 significant figures.
- 1 kg m⁻³ = 10³ g cm⁻³
- Maximum percentage error in a physical quantity is given by ((3∆x/x) + (2∆y/y) + (∆z/2z)) x 100.
- Dimensionally incorrect equations can never be physically correct.
- Physically correct equations must be dimensionally correct.
- Strain and angle have the same dimensions as those of solid angles.
- In a vernier calipers, (N+1) divisions of vernier scale coincide with N divisions of the main scale.
- If 1 MSD represents 0.1 mm, the vernier constant (in cm) is equal to 1/(10(N+1)).
- A force is defined by F=αt² + βt acts on a particle at a given time t.
- The factor at/β is dimensionless, if α and β are dimensional constants.
- Errors in measurement that arise due to unpredictable fluctuations in temperature and voltage supply are random errors.
- Plane angle has units but no dimensions.
- The percentage error in the measurement of g is 3%, given that g = 4π²L/T², L=(10±0.1)cm, and T=(100±1).
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