In the experiment of simple pendulum error in length of pendulum (ℓ) is 5 % and that of g is 3 %

step 1 Okay, the question is acceleration due to gravity is given by G equal to Gm out of R squared. So

In the experiment of simple pendulum error in length of...

In the experiment of simple pendulum error in length of pendulum $(\ell)$ is $5 \%$ and that of $g$ is $3 \%$ then find percentage error in measurement of periodic time for pendulum
(a) $4.2 \%$
(b) $1.2 \%$
(c) $2 \%$
(d) $4 \%$

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Key Concepts

Simple Pendulum Period Formula

The period of a simple pendulum is given by T = 2??(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. This formula establishes how the period depends on these factors and is fundamental for studying the dynamics of pendulums as well as for deriving related error propagation formulas.

Uncertainty Propagation

When measurements with errors are used in calculations, the resulting uncertainty in a computed value can be determined by propagating the errors from the measured quantities through the mathematical relationship. This is typically achieved by combining the relative (or percent) errors appropriately, depending on how the measured quantities contribute to the final expression.

Error Propagation with Exponents

For parameters that appear with an exponent in a formula, such as the square root in T = 2??(l/g), the relative error of that variable is multiplied by the exponent (in this case, 1/2). This principle simplifies the handling of errors in non-linear equations by using rules derived from logarithmic differentiation.

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