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

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(B) The formula for the time period of a simple pendulum is $T = 2\pi \sqrt{\frac{L}{g}}$.Squaring both sides,we get $T^2 = 4\pi^2 \frac{L}{g}$,which implies $g = 4\pi^2 \frac{L}{T^2}$.The relative error in $g$ is given by $\frac{\Delta g}{g} = \frac{\Delta L}{L} + 2 \frac{\Delta T}{T}$.Given: $L = 20.0$ cm,$\Delta L = 1$ mm = $0.1$ cm.$T_{total} = 90.0$ s,$\Delta T_{total} = 1$ s. Since $T = \frac{T_{total}}{100}$,$\Delta T = \frac{\Delta T_{total}}{100} = \frac{1}{100} = 0.01$ s.Substituting the values:$\frac{\Delta g}{g} = \frac{0.1}{20.0} + 2 \times \frac{1}{90} = 0.005 + 0.0222 = 0.0272$.Percentage error = $0.0272 \times 100 = 2.72 \% \approx 2.7 \%$.

Class 11 Physics Units, Dimensions and Measurement Errors of Measurement

Difficult

An experiment is performed to obtain the value of acceleration due to gravity $g$ by using a simple pendulum of length $L$. In this experiment,the time for $100$ oscillations is measured by using a watch of $1$ second least count,and the value is $90.0$ seconds. The length $L$ is measured by using a meter scale of least count $1$ mm,and the value is $20.0$ cm. The error in the determination of $g$ would be ........... $\%$.

JEE MAIN 2014 All JEE MAIN

A
$1.7$
B
$2.7$
C
$4.4$
D
$2.27$

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Units, Dimensions and Measurement

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Errors of Measurement

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JEE MAIN 2014 Paper All JEE MAIN years →

The radius $(r)$,length $(l)$,and resistance $(R)$ of a metal wire were measured in the laboratory as:
$r = (0.35 \pm 0.05) \text{ cm}$
$R = (100 \pm 10) \text{ } \Omega$
$l = (15 \pm 0.2) \text{ cm}$
The percentage error in the resistivity of the material of the wire is: (in $\%$)

DifficultJEE MAIN 2024

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In an experiment for the measurement of $g$ using a simple pendulum,the time period was measured with an accuracy of $0.2 \%$ while the length was measured with an accuracy of $0.5 \%$. The percentage accuracy in the value of $g$ thus obtained is: (in $\%$)

MediumMHT CET 2020

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Two resistances are measured in $\Omega$ and are given as $R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$. When they are connected in parallel,the percentage error in equivalent resistance is .......... $\%$

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The period of oscillation of a simple pendulum is $T = 2 \pi \sqrt{\frac{L}{g}}$. The measured value of $L$ is $1.0 \text{ m}$ using a meter scale with a minimum division of $1 \text{ mm}$,and the time for one complete oscillation is $1.95 \text{ s}$ measured using a stopwatch with a resolution of $0.01 \text{ s}$. The percentage error in the determination of $g$ will be ..... $\%$.

MediumJEE MAIN 2021

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The two specific heat capacities of a gas are measured as $C_P = (12.28 \pm 0.2) \text{ units}$ and $C_V = (3.97 \pm 0.3) \text{ units}$. Find the value of the gas constant $(R)$.

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The radius $(r)$,length $(l)$,and resistance $(R)$ of a metal wire were measured in the laboratory as:$r = (0.35 \pm 0.05) \text{ cm}$$R = (100 \pm 10) \text{ } \Omega$$l = (15 \pm 0.2) \text{ cm}$The percentage error in the resistivity of the material of the wire is: (in $\%$)

In an experiment for the measurement of $g$ using a simple pendulum,the time period was measured with an accuracy of $0.2 \%$ while the length was measured with an accuracy of $0.5 \%$. The percentage accuracy in the value of $g$ thus obtained is: (in $\%$)

Two resistances are measured in $\Omega$ and are given as $R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$. When they are connected in parallel,the percentage error in equivalent resistance is .......... $\%$

The two specific heat capacities of a gas are measured as $C_P = (12.28 \pm 0.2) \text{ units}$ and $C_V = (3.97 \pm 0.3) \text{ units}$. Find the value of the gas constant $(R)$.

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The radius $(r)$,length $(l)$,and resistance $(R)$ of a metal wire were measured in the laboratory as:
$r = (0.35 \pm 0.05) \text{ cm}$
$R = (100 \pm 10) \text{ } \Omega$
$l = (15 \pm 0.2) \text{ cm}$
The percentage error in the resistivity of the material of the wire is: (in $\%$)