If $x = a -b,$ then percentage error in $x$ will be
If $x = a -b,$ then percentage error in $x$ will be
- A
$\left( {\frac{{\Delta a}}{a} + \frac{{\Delta b}}{b}} \right) \times 100\,\% $
- B
$\left( {\frac{{\Delta a}}{a} - \frac{{\Delta b}}{b}} \right) \times 100\,\% $
- C
$\left( {\frac{{\Delta a}}{a-b} + \frac{{\Delta b}}{a-b}} \right) \times 100\,\% $
- D
$\left( {\frac{{\Delta a}}{a-b} - \frac{{\Delta b}}{a-b}} \right) \times 100\,\% $
Similar Questions
The mean time period of second's pendulum is $2.00s$ and mean absolute error in the time period is $0.05s$. To express maximum estimate of error, the time period should be written as
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Explain effect of multiplication or division of error on final result.
Explain effect of multiplication or division of error on final result.
In a simple pendulum experiment for determination of acceleration due to gravity $(g)$, time taken for $20$ oscillations is measured by using a watch of $1\, second$ least count. The mean value of time taken comes out to be $30\,s$. The length of pendulum is measured by using a meter scale of least count $1\, mm$ and the value obtained is $55.0\, cm$. The percentage error in the determination of $g$ is close to ........... $\%$
In a simple pendulum experiment for determination of acceleration due to gravity $(g)$, time taken for $20$ oscillations is measured by using a watch of $1\, second$ least count. The mean value of time taken comes out to be $30\,s$. The length of pendulum is measured by using a meter scale of least count $1\, mm$ and the value obtained is $55.0\, cm$. The percentage error in the determination of $g$ is close to ........... $\%$
- [JEE MAIN 2019]
In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \mathrm{mm}$ and $(10 \pm 1) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{~s}, 0.56 \mathrm{~s}, 0.57 \mathrm{~s}, 0.54 \mathrm{~s}$ and $0.59 \mathrm{~s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{~s}$. Which of the following statement($s$) is(are) true?
($A$) The error in the measurement of $r$ is $10 \%$
($B$) The error in the measurement of $T$ is $3.57 \%$
($C$) The error in the measurement of $T$ is $2 \%$
($D$) The error in the determined value of $g$ is $11 \%$
In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \mathrm{mm}$ and $(10 \pm 1) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{~s}, 0.56 \mathrm{~s}, 0.57 \mathrm{~s}, 0.54 \mathrm{~s}$ and $0.59 \mathrm{~s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{~s}$. Which of the following statement($s$) is(are) true?
($A$) The error in the measurement of $r$ is $10 \%$
($B$) The error in the measurement of $T$ is $3.57 \%$
($C$) The error in the measurement of $T$ is $2 \%$
($D$) The error in the determined value of $g$ is $11 \%$
- [IIT 2016]
If the random error in the arithmetic mean of $50$ observations is $\alpha$, then the random error in the arithmetic mean of $150$ observations would be
If the random error in the arithmetic mean of $50$ observations is $\alpha$, then the random error in the arithmetic mean of $150$ observations would be