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Chapter 1: Problem 93

The percentage error in the distance \(100 \pm 5 \mathrm{~cm}\) is ... (a) \(5 \%\) (b) \(6 \%\) (c) \(8 \%\) (d) \(20 \%\)

Short Answer

Expert verified
The percentage error in the distance \(100 \pm 5 \mathrm{~cm}\) is (a) \(5\%\).

Step by step solution

01

Identify the Error and Measured Value

The given distance is \(100 \pm 5\mathrm{~cm}\). Hence, the measured value is \(100\mathrm{~cm}\) and the error is \(5\mathrm{~cm}\).
02

Calculate Percentage Error

Using the formula, we can calculate the percentage error as follows: \[Percentage \ Error = \frac{Error}{Measured\ Value} \times 100\%\] Plug in the values of Error and Measured Value: \[Percentage \ Error = \frac{5\mathrm{~cm}}{100\mathrm{~cm}}\times 100\% \]
03

Simplify the expression

Now, simplify the expression: \[Percentage \ Error = \frac{5}{100}\times 100\%\] \[Percentage \ Error = 0.05\times 100\%\] \[Percentage \ Error = 5\%\] The percentage error is \(5\%\). Therefore, the correct answer is (a) \(5\%\).

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Most popular questions from this chapter

Dimensions of impulse are. (a) \(\mathrm{M}^{-1} \mathrm{~L}^{-1} \mathrm{~T}^{1}\) (b) $\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-1}$ (c) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{1}\) (d) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}\)

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