1. The respective number of significant figures for the numbers $23.023$, $0.0003$ and $2.1 \times 10^{-3}$ are:
Verification Matrix:
For $23.023$, all 5 digits are significant (including the trapped zero). For $0.0003$, leading zeros are purely placeholders to fix the decimal point, leaving 1 significant figure. For $2.1 \times 10^{-3}$, base-10 exponential factors do not contribute to precision, leaving exactly 2 significant figures.
2. Which among the following is the supplementary unit:
Verification Matrix:
While mass, time, and luminosity are base/fundamental SI units, geometric variables like plane angle (measured in radians) and solid angle (measured in steradians) are classified separately as supplementary units.
3. The unit of solid angle is:
Verification Matrix:
The steradian ($\text{sr}$) is specifically defined as the 3-dimensional SI supplementary unit for solid angles, whereas second is for time, kilogram is for mass, and candela is for luminous intensity.
4. The quantity having the same unit in all system of units is:
Verification Matrix:
Across all historic measurement systems—including CGS (Centimeter-Gram-Second), MKS (Meter-Kilogram-Second), FPS (Foot-Pound-Second), and the modern International System (SI)—the standard unit for time remains identical: the second ($\text{s}$).
5. Random errors can be eliminated by:
Verification Matrix:
Random errors occur unpredictably due to small, random fluctuations in environmental or experimental criteria. Because they are statistically symmetric, taking a high volume of independent observations and calculating their arithmetic mean minimizes their impact on accuracy.
6. Systematic error can be:
Verification Matrix:
Systematic errors occur in a uniform direction due to an underlying bias (like faulty scale calibration or zero errors). Depending on whether the device consistently overestimates or underestimates, the systematic deviation can be strictly positive or strictly negative.
7. $\text{[MLT}^{-2}\text{]}$ is the dimensional formula of:
Verification Matrix:
By applying Newton's Second Law: $\text{Force} = \text{Mass} \times \text{Acceleration}$. Substituting base structural variables gives $\text{[M]} \times \text{[LT}^{-2}\text{]} = $ [MLT⁻²].
8. Which of the following pairs has the same dimension?
Verification Matrix:
According to the impulse-momentum theorem, the Impulse applied to an object changes its linear momentum. Both quantities share identical base units ($\text{kg}\cdot\text{m}\cdot\text{s}^{-1}$) and identical structural dimensions: [MLT⁻¹].
9. Dependent variable is the:
Verification Matrix:
In empirical physics analysis, the parameter explicitly altered by the experimenter acts as the 'cause' (independent variable), whereas the parameter that responds dynamically acts as the measurable 'effect' (dependent variable).
10. Dimensions of kinetic energy is the same as that of:
Verification Matrix:
According to the Work-Energy Theorem, work and energy are fully equivalent expressions. They can be parsed into identical mechanical structural configurations with a dimensional signature of [ML²T⁻²].
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