The period of oscillation of a simple pendulum is T=2 π√((L)/(g)) . Measured value of L is 20.0

step 1 In this question we will learn about some basic concept of the units and measurement. The questi

The period of oscillation of a simple pendulum is T=2...

The period of oscillation of a simple pendulum is $T=2 \pi \sqrt{\frac{L}{g}} .$ Measured value of $L$ is $20.0 \mathrm{~cm}$ known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of $g$ is (A) $3 \%$ (B) $1 \%$ (C) $5 \%$ (D) $2 \%$

Key Concepts

Simple Pendulum Oscillation

This concept involves understanding that a simple pendulum exhibits periodic motion described by the formula T = 2? ?(L/g), where T is the period of oscillation, L is the length of the pendulum, and g is the acceleration due to gravity. It encapsulates the idea that the period depends on the square root of the length and is inversely related to the square root of the gravitational acceleration, assuming small-angle approximations.

Error Propagation

Error propagation is the process used in experimental physics to determine how uncertainties in measured quantities (such as length and time) affect the final uncertainty in a derived quantity, like gravitational acceleration. This involves using mathematical formulas to combine relative or absolute uncertainties through operations such as multiplication, division, or taking roots.

Instrument Resolution and Accuracy

Instrument resolution refers to the smallest increment that a measuring device can reliably detect, while accuracy indicates how close a measurement is to the true value. Both aspects are essential because the finite resolution of measurement instruments contributes to the uncertainty in experimental data, influencing the reliability of the derived results.

Percentage Error Calculation

Percentage error is a method of expressing the uncertainty of a measurement as a fraction of the measured value, multiplied by 100 to yield a percentage. It provides a normalized indication of error magnitude, facilitating comparisons across different experiments and variables.

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