The periodic time of simple pendulum is T=2 π√((ℓ/ g)) relative error in the measurement of T an

step 1 Okay, in this question we have to find out the relative error in G when the time period of pendu

The periodic time of simple pendulum is T=2 π√((ℓ/ g))...

The periodic time of simple pendulum is $\mathrm{T}=2 \pi \sqrt{(\ell / \mathrm{g})}$ relative error in the measurement of $\mathrm{T}$ and $\ell$ are $\pm \mathrm{a}$ and $\pm \mathrm{b}$ respectively find relative error in the measurement of $g$ (a) $a+b$ (b) $2 \mathrm{~b}+\mathrm{a}$ (c) $2 \mathrm{a}+\mathrm{b}$ (d) $a-b$

The periodic time of simple pendulum is $\mathrm{T}=2 \pi \sqrt{(\ell / \mathrm{g})}$ relative error in the measurement of $\mathrm{T}$ and $\ell$ are $\pm \mathrm{a}$ and $\pm \mathrm{b}$ respectively find relative error in the measurement of $g$
(a) $a+b$
(b) $2 \mathrm{~b}+\mathrm{a}$
(c) $2 \mathrm{a}+\mathrm{b}$
(d) $a-b$

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Key Concepts

Relative Error

Relative error represents the size of the error in comparison to the true value and is usually expressed as a fraction or percentage. It is a useful measure because it provides a normalized way to compare uncertainties in different contexts or scales.

Error Propagation

Error propagation is the process of determining the uncertainty in a function based on the uncertainties in its input quantities. This is typically achieved using techniques such as partial derivatives or logarithmic differentiation to understand how errors in measurements affect the final computed result.

Logarithmic Differentiation

Logarithmic differentiation is a method used in error analysis to simplify the process of finding relative errors. By taking the natural logarithm of a function and differentiating, multiplicative relationships are transformed into additive relationships, making it easier to determine how the relative errors in individual variables combine to affect the overall error in the computed quantity.

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