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Units and Measurement question

2010 · Q101
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Units and Measurement question

2010 · Q101

NEETPhysicsUnits and MeasurementMCQ+4 / −1
A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is
  1. A
    e2 −-− e1
  2. B
    e1 + 2e2
  3. C
    e1 + e2
  4. D
    e1 −-− 2e2
View written solutionFree

Correct answer: B

Initially body is at rest.

∴\therefore∴ h=12gt2h = {1 \over 2}g{t^2}h=21​gt2

⇒\Rightarrow⇒ g=2ht2g = {{2h} \over {{t^2}}}g=t22h​

Maximum percentage error,

Δgg×100=[Δhh+2Δtt]×100{{\Delta g} \over g} \times 100 = \left[ {{{\Delta h} \over h} + 2{{\Delta t} \over t}} \right] \times 100gΔg​×100=[hΔh​+2tΔt​]×100

Given that
Δhh×100{{{\Delta h} \over h} \times 100}hΔh​×100 = e1

and Δtt×100{{{\Delta t} \over t} \times 100}tΔt​×100 = e2

∴\therefore∴ Δgg×100{{\Delta g} \over g} \times 100 gΔg​×100 = e1 + 2e2

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