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The density of a solid ball is to be determined in anexperiment. The diameter of the ball is measuredwith a screw gauge, whose pitch is 0.5 mm and thereare 50 divisions on the circular scale. The readingon the main scale is 2.5 mm and that on the circularscale is 20 divisions. If the measured mass of theball has a relative error of 2%, the relative percentageerror in the density is
  • a)
    0.9%
  • b)
    2.4%
  • c)
    3.1%
  • d)
    4.2%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The density of a solid ball is to be determined in anexperiment. The d...
so the diameter is = 2.5 + (0.5/50 x 20) = 2.7 
the error in diameter estimation is δr =0.01 mm
δD/D = 0.01/2.7 = 0.0037
now ρ =m/v
ln(ρ )= ln m + ln (4/3π(D/2)^3)
δρ/ρ = δm/m + 3 (δD/D)
δρ/ρ = 3.1%
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The density of a solid ball is to be determined in anexperiment. The diameter of the ball is measuredwith a screw gauge, whose pitch is 0.5 mm and thereare 50 divisions on the circular scale. The readingon the main scale is 2.5 mm and that on the circularscale is 20 divisions. If the measured mass of theball has a relative error of 2%, the relative percentageerror in the density isa)0.9%b)2.4%c)3.1%d)4.2%Correct answer is option 'C'. Can you explain this answer?
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The density of a solid ball is to be determined in anexperiment. The diameter of the ball is measuredwith a screw gauge, whose pitch is 0.5 mm and thereare 50 divisions on the circular scale. The readingon the main scale is 2.5 mm and that on the circularscale is 20 divisions. If the measured mass of theball has a relative error of 2%, the relative percentageerror in the density isa)0.9%b)2.4%c)3.1%d)4.2%Correct answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The density of a solid ball is to be determined in anexperiment. The diameter of the ball is measuredwith a screw gauge, whose pitch is 0.5 mm and thereare 50 divisions on the circular scale. The readingon the main scale is 2.5 mm and that on the circularscale is 20 divisions. If the measured mass of theball has a relative error of 2%, the relative percentageerror in the density isa)0.9%b)2.4%c)3.1%d)4.2%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The density of a solid ball is to be determined in anexperiment. The diameter of the ball is measuredwith a screw gauge, whose pitch is 0.5 mm and thereare 50 divisions on the circular scale. The readingon the main scale is 2.5 mm and that on the circularscale is 20 divisions. If the measured mass of theball has a relative error of 2%, the relative percentageerror in the density isa)0.9%b)2.4%c)3.1%d)4.2%Correct answer is option 'C'. Can you explain this answer?.
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