(A) The time period $T$ of a simple pendulum is given by the formula: $T = 2\pi \sqrt{\frac{L}{g}}$.Squaring both sides,we get: $T^2 = 4\pi^2 \frac{L}

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(A) The time period $T$ of a simple pendulum is given by the formula: $T = 2\pi \sqrt{\frac{L}{g}}$.Squaring both sides,we get: $T^2 = 4\pi^2 \frac{L}{g}$.Rearranging for $g$: $g = 4\pi^2 \frac{L}{T^2}$.The relative error in $g$ is given by: $\frac{\Delta g}{g} = \frac{\Delta L}{L} + 2 \frac{\Delta T}{T}$.Given that $\alpha = \frac{\Delta L}{L}$ and $\beta = \frac{\Delta T}{T}$,the relative error in $g$ is $\alpha + 2\beta$.To find the percentage error,we multiply by $100$: $\text{Percentage error} = (\alpha + 2\beta) \times 100$.

Class 11 Physics Units and Measurements Errors of Measurement

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The acceleration due to gravity is measured on the surface of the Earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively,then the percentage error in the measurement of acceleration due to gravity is:

A
$(\alpha + 2\beta) \times 100$
B
$(\alpha - 2\beta) \times 100$
C
$(2\alpha + \beta) \times 100$
D
$(\alpha + \frac{1}{2}\beta) \times 100$

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Errors of Measurement

$A$ torque meter is calibrated to reference standards of mass,length,and time,each with $5 \%$ accuracy. After calibration,the measured torque with this torque meter will have a net accuracy of $............\%$.

MediumJEE MAIN 2022

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In an experiment,four quantities $a, b, c, d$ are measured with percentage errors $2\%$,$1\%$,$3\%$ and $5\%$,respectively. Quantity $P$ is calculated as $P = \frac{a^2 b^2}{c d}$. Find the percentage error in measuring $P$. (in $\%$)

EasyAP EAMCET 2021

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$A$ quantity $Q$ is formulated as $Q = X^{-2} Y^{\frac{3}{2}} Z^{-\frac{2}{5}}$. $X, Y$ and $Z$ are independent parameters which have fractional errors of $0.1, 0.2$ and $0.5$,respectively,in measurement. The maximum fractional error of $Q$ is:

EasyJEE MAIN 2025

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If $Q = \frac{X^n}{Y^m}$ and $\Delta X$ is the absolute error in the measurement of $X$,and $\Delta Y$ is the absolute error in the measurement of $Y$,then the absolute error $\Delta Q$ in $Q$ is:

Easy

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The density of a cube is determined by measuring its mass and the length of its sides. The percentage errors in the measurement of mass and length are $5 \%$ and $6 \%$ respectively. The percentage error in the measurement of density is (in $\%$):

DifficultMHT CET 2025

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The acceleration due to gravity is measured on the surface of the Earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively,then the percentage error in the measurement of acceleration due to gravity is:

Similar Questions

$A$ torque meter is calibrated to reference standards of mass,length,and time,each with $5 \%$ accuracy. After calibration,the measured torque with this torque meter will have a net accuracy of $............\%$.

In an experiment,four quantities $a, b, c, d$ are measured with percentage errors $2\%$,$1\%$,$3\%$ and $5\%$,respectively. Quantity $P$ is calculated as $P = \frac{a^2 b^2}{c d}$. Find the percentage error in measuring $P$. (in $\%$)

$A$ quantity $Q$ is formulated as $Q = X^{-2} Y^{\frac{3}{2}} Z^{-\frac{2}{5}}$. $X, Y$ and $Z$ are independent parameters which have fractional errors of $0.1, 0.2$ and $0.5$,respectively,in measurement. The maximum fractional error of $Q$ is:

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