Give answer to any eight short questions of the following: 1. Define precision and accuracy. 2. Give dimensions of pressure and density. 3. How uncertainty can be reduced in the ti... Give answer to any eight short questions of the following: 1. Define precision and accuracy. 2. Give dimensions of pressure and density. 3. How uncertainty can be reduced in the timing experiment? 4. Show that the expression v_f = v_i + a t is dimensionally correct. 5. How will you access the total uncertainty in case of power factor? Give an example. 6. Given that V = (5.2 ± 0.1) volt. Find its percentage uncertainty. 7. How many seconds are there in one year? 8. Write down the two uses of dimensional analysis. 9. Dimensionally prove E = mc^2.
Understand the Problem
The question is asking to provide answers for any eight out of nine short questions related to precision, accuracy, dimensions, uncertainty, and equations in physics.
Answer
["Precision: consistency; Accuracy: closeness to true value.","Pressure: ML^-1T^-2; Density: ML^-3.","Use precise devices or average results.","v_f = v_i + at is dimensionally correct.","Combine uncertainties relative to power factor.","1.923% uncertainty for 5.2 \u00b1 0.1 V.","31,536,000 seconds\/year.","Checks consistency; converts units.","E = mc^2: consistent with ML^2T^-2."]
["1. Precision is the consistency of repeated measurements, whereas accuracy is how close a measurement is to the true value.","2. The dimensions of pressure are ML^-1T^-2 and those of density are ML^-3.","3. Uncertainty in timing experiments can be reduced by using more precise instruments or averaging multiple measurements.","4. The equation v_f = v_i + at is dimensionally consistent; it fits velocity dimensions, LT^-1.","5. Total uncertainty can be calculated by combining individual uncertainties; e.g., for power factor, sum relative uncertainties.","6. Percentage uncertainty for V = (5.2 \u00b1 0.1) V is 1.923%.","7. There are 31,536,000 seconds in one year.","8. Dimensional analysis is used for checking dimensional consistency and unit conversions.","9. Both sides of E = mc^2 have dimensions ML^2T^-2, proving dimensional consistency."]
Answer for screen readers
["1. Precision is the consistency of repeated measurements, whereas accuracy is how close a measurement is to the true value.","2. The dimensions of pressure are ML^-1T^-2 and those of density are ML^-3.","3. Uncertainty in timing experiments can be reduced by using more precise instruments or averaging multiple measurements.","4. The equation v_f = v_i + at is dimensionally consistent; it fits velocity dimensions, LT^-1.","5. Total uncertainty can be calculated by combining individual uncertainties; e.g., for power factor, sum relative uncertainties.","6. Percentage uncertainty for V = (5.2 \u00b1 0.1) V is 1.923%.","7. There are 31,536,000 seconds in one year.","8. Dimensional analysis is used for checking dimensional consistency and unit conversions.","9. Both sides of E = mc^2 have dimensions ML^2T^-2, proving dimensional consistency."]
More Information
Each concept here involves fundamental principles of physics, including measurement strategies and mathematical verifications for concepts like Einstein's mass-energy equivalence.
Tips
Common mistakes include mixing units or misunderstanding dimensional consistency, especially in equations.
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