Question 216: Units , Dimensions and Error Analysis

Question

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of $$0.5 \mathrm{~s}$$ is measured from time of 100 oscillation with a watch of $$1 \mathrm{~s}$$ resolution. If measured value of length is $$10 \mathrm{~cm}$$ known to $$1 \mathrm{~mm}$$ accuracy, The accuracy in the determination of $$\mathrm{g}$$ is found to be $$x \%$$. The value of $$x$$ is ___________.

Accepted Answer

$$T = 2\pi \sqrt {{l \over g}} $$
$${{dg} \over g} 	imes 100 = {{2dT} \over T} 	imes 100 + {{dl} \over l} 	imes 100$$
$$ = 2 	imes {1 \over {50}} 	imes 100 + {1 \over {100}} 	imes 100 = 5\% $$

Units , Dimensions and Error Analysis

Integer / Numeric Answer Type