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Units and Measurement question

2022 · Q172
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Units and Measurement question

2022 · Q172

NEETPhysicsUnits and MeasurementMCQ+4 / −1

The percentage error in the measurement of g is : (Given that g=4π2LT2g = {{4{\pi ^2}L} \over {{T^2}}}g=T24π2L​, L=(10 ± 0.1)L = (10\, \pm \,0.1)L=(10±0.1) cm, T=(100 ± 1)T = (100\, \pm \,1)T=(100±1) s)

  1. A
    7%
  2. B
    2%
  3. C
    5%
  4. D
    3%
View written solutionFree

Correct answer: D

Given $$g = {{4{p^2}L} \over {{T^2}}}$$

Fractional error in value of g

$${{\Delta g} \over g} = {{\Delta L} \over L} + 2{{\Delta T} \over T}$$

$$ \Rightarrow {{\Delta g} \over g} \times 100 = {{\Delta L} \over L} \times 100 + 2{{\Delta T} \over T} \times 100$$

$$ \Rightarrow {{\Delta g} \over g} \times 100 = {{0.1} \over {10}} \times 100 + 2 \times {1 \over {100}} \times 100 = 3\% $$

Hence, percentage error in measurement of g is 3%

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