CHAPTER NO 1 MEASUREMENTS PRACTICE MCQS SOLUTION FROM NOTES PHYSICS INN-ABDULLAH

 

Topic 1.1: Physical Quantities and Their Units

Answer Key with Hints/Solutions

1. (b) Sol: Base quantities are defined independently and serve as the foundation to define other quantities.
2. (b) Sol: Measurement of a base quantity requires two steps: choice of a standard and establishing a comparison procedure.
3. (b) Sol: Velocity, acceleration, and force all depend on fundamental base quantities (length, mass, time).
4. (b) Sol: The comparison procedure determines a numerical magnitude and a unit as the measure of the quantity.
5. (b) Sol: Derived quantities are defined in terms of base physical quantities.
6. (b) Sol: Laws of physics express relationships between measurable physical quantities to describe nature objectively.
7. (b) Sol: Any physical quantity defined through a combination or ratio of other physical quantities is derived.
8. (b) Sol: The comparison procedure determines how many standard units are present in the unknown quantity.
9. (b) Sol: Base quantities are independent foundation blocks; derived quantities rely on base quantities.
10. (a) Sol: Classification as base or derived depends on theoretical independence, not on whether an instrument can measure it directly.
11. (b) Sol: The numerical value is the ratio comparing the measured quantity to the unit standard.
12. (b) Sol: The primary step in measuring any base quantity is selecting a standard.
13. (b) Sol: Time is an independent base quantity, whereas speed is a derived quantity (length/time).
14. (b) Sol: Density () depends on the base quantities mass and length.
15. (b) Sol: Selecting a reference block serves as the first step in measurement: choice of a standard.

 

Topic 1.2: International System of Units

1. (b) Sol: The international committee agreed on the System International (SI) in 1960.
2. (c) Sol: Unit symbols named after scientists are written in capital letters (kelvin ).
3. (b) Sol: Steradian () is the SI unit for solid angle.
4. (b) Sol: Femto () corresponds to .
5. (b) Sol: SI units are represented by strict symbols (, ) and not abbreviations.
6. (c) Sol: A power applied to a unit with a prefix applies to the whole multiple ().
7. (b) Sol: Compound prefixes are not allowed;  must be written as .
8. (b) Sol: Full names of units do not begin with a capital letter, even if named after a scientist.
9. (c) Sol: Scientific notation requires exactly one non-zero digit to the left of the decimal ().
10. (b) Sol: The bar (and millibar) is a permitted pressure unit in meteorology.
11. (b) Sol: .
12. (b) Sol: Mixing names and symbols (metre/sec) is prohibited; use  or metre per second.
13. (c) Sol: .
14. (b) Sol: .
15. (b) Sol:  in standard form.

 

Topic 1.3: Uncertainty in Measurement

Answer Key with Hints/Solutions

1. (b) Sol: Absolute uncertainty equals the smallest division (least count) of the instrument scale.
2. (b) Sol: By definition, .
3. (b) Sol: Large fluctuations () indicate external disturbances like air currents affecting the display.
4. (b) Sol: .
5. (b) Sol: Instruments are calibrated to finite graduation marks, limiting precise scale reading.
6. (b) Sol: A smaller least count directly reduces the absolute uncertainty of the measurement.
7. (b) Sol: Position uncertainties of  at both initial and final marks add up: .
8. (b) Sol: A smaller percentage uncertainty means the error is a smaller fraction of the measured value, increasing accuracy.
9. (b) Sol: If fluctuation is 1 or 2 in the last digit of a digital scale, write down that last digit.
10. (c) Sol:  (least count of millimeter ruler).
11. (b) Sol: Increasing the measured magnitude () in  decreases the percentage uncertainty.
12. (a) Sol: .
13. (b) Sol: .
14. (c) Sol: .
15. (b) Sol: .

 

Topic 1.4: Use of Significant Figures

Answer Key with Hints/Solutions

1. (c) Sol: Significant figures include all accurately known digits plus the first doubtful/estimated digit.
2. (b) Sol: Zeros located between two significant figures are always significant.
3. (c) Sol: If the dropped digit is 5, an odd preceding digit is increased by 1 (e.g., 3 becomes 4).
4. (b) Sol: For multiplication/division, the quotient or product retains the same number of sig figs as the factor with the least accuracy (fewest sig figs).
5. (b) Sol: Leading zeros to the left of the first non-zero digit merely indicate the place of the decimal point.
6. (b) Sol: Writing values as  specifies exactly 3 significant figures without ambiguity.
7. (b) Sol: For addition/subtraction, the result takes the smallest number of decimal places present in any term.
8. (b) Sol: Significant figures reflect scale limitations but cannot account for personal biases or hidden systematic errors.
9. (b) Sol: Quoting more significant digits reflects a measurement made with a higher-precision instrument.
10. (b) Sol: Dropping 5 after 3 (odd) increases the retained digit by 1 to yield .
11. (a) Sol: Dropping 5 after 6 (even) leaves the retained digit unchanged as .
12. (c) Sol: Leading zeros are non-significant;  are 4 significant figures.
13. (c) Sol: ; least accurate factor () has 2 sig figs, so round to .
14. (c) Sol: ; least precise quantity () has 0 decimal places, so round to .
15. (b) Sol: ;  has 1 decimal place, so round to .

 

Topic 1.5: Precision and Accuracy

Answer Key with Hints/Solutions

1. (c) Sol: Precision is determined directly by the instrument's least count or absolute uncertainty.
2. (b) Sol: Accuracy is quantified by relative measurement errors, i.e., fractional or percentage uncertainty.
3. (b) Sol: A smaller absolute uncertainty (least count) indicates higher precision.
4. (a) Sol: A smaller percentage uncertainty means the measurement is closer to the true value (higher accuracy).
5. (b) Sol: Precision depends on absolute uncertainty (), whereas accuracy depends on fractional/percentage uncertainty ().
6. (a) Sol: Percentage uncertainty depends on total measured magnitude; a large measured value can yield a small percentage error even with a larger least count.
7. (b) Sol: For small magnitudes, fractional uncertainty  becomes large unless absolute uncertainty  is made very small.
8. (b) Sol: Low absolute uncertainty means high precision, but high percentage uncertainty means low accuracy.
9. (b) Sol:  has , while  has ; less  uncertainty means higher accuracy.
10. (c) Sol: To measure a small length () accurately, an instrument with a very small least count () is required to keep percentage error low.
11. (b) Sol: Uncorrected zero error shifts readings away from the true value (reducing accuracy) without altering the instrument's least count (precision remains unchanged).
12. (a) Sol: .
13. (c) Sol: .
14. (b) Sol: ; . Lower  error means higher accuracy.
15. (b) Sol: .

 

 

Topic 1.6: Assessment of Total Uncertainty in the Final Result

Answer Key with Hints/Solutions

1. (a) Sol: For addition and subtraction, absolute uncertainties of all quantities are added directly.
2. (b) Sol: For multiplication and division, percentage uncertainties are added together.
3. (c) Sol: Total percentage uncertainty .
4. (b) Sol: Uncertainty estimates are usually rounded to one significant figure in standard practice.
5. (b) Sol: Uncertainties represent worst-case error bounds; taking differences does not eliminate measurement error, so absolute errors accumulate.
6. (b) Sol: Total percentage error  due to power factor 3.
7. (b) Sol: In , radius has a power factor of 2, which doubles its percentage uncertainty contribution.
8. (b) Sol: For , total percentage uncertainty .
9. (b) Sol: ; .
10. (b) Sol: .
11. (c) Sol: ; absolute uncertainty .
12. (c) Sol: ; ; Total .
13. (b) Sol: ; Total .
14. (c) Sol: ; ; Total .
15. (c) Sol: .

 

 

Topic 1.7: Dimensions of Physical Quantities

Answer Key with Hints/Solutions

1. (b) Sol: Thermodynamic temperature is denoted by the dimension symbol .
2. (b) Sol: .
3. (b) Sol: By the Principle of Homogeneity, both sides of a valid physical equation must have identical dimensions.
4. (b) Sol: Dimensional analysis cannot yield the value of dimensionless constants (like  or ).
5. (b) Sol: Pure numbers have no physical units or qualitative dimensions ().
6. (b) Sol: Dimensional correctness is necessary but not sufficient; numerical constants cannot be verified.
7. (b) Sol: Only physical quantities representing the same qualitative property (same dimensions) can be added or subtracted.
8. (b) Sol: .
9. (a) Sol: .
10. (a) Sol: Both work () and torque () have dimensions .
11. (b) Sol: .
12. (b) Sol: Comparing time powers in  gives .
13. (b) Sol: .
14. (b) Sol: ; .
15. (a) Sol: .