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AIIMS 201827 May
Exam
AIIMS
Year
2018
Date
27 May
Subject
Physics
Chapter
Mathematics in Physics

AIIMS 2018 · 27 May · Physics · Mathematics in Physics

The percentage error in measuring M, L and T are 1 \%, 1.5 \% and 3...

The percentage error in measuring M,L\mathrm{M}, \mathrm{L} and T\mathrm{T} are 1%,1.5%and3%1 \%, 1.5 \% and 3 \% respectively. Then the percentage error in measuring the physical quantity with dimensions [ML−1 T−1]\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right] is

Options

  1. A1%1 \%
  2. B3.5%3.5 \%
  3. C3%3 \%
  4. D5.5%5.5 \%

Correct answer

D. 5.5%5.5 \%

Step-by-step solution

( Let X=X=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]PercentageerrorinPercentage error inXisis\frac{\Delta X}{X} \times 100=\left(\frac{\Delta M}{M}+\frac{\Delta L}{L}+\frac{\Delta T}{T}\right) \times 100Here,Here,\frac{\Delta M}{M} \times 100=1 \%, \frac{\Delta L}{L} \times 100=1.5 \%andandΔTT×100=3%∴ΔXX×100=1%+1.5%+3%=5.5%\begin{aligned} & \frac{\Delta T}{T} \times 100=3 \% \\ & \therefore \quad \frac{\Delta X}{X} \times 100=1 \%+1.5 \%+3 \%=5.5 \%\end{aligned}$
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