question_answer

For the determination of ?g? using a simple pendulum, measurements of \[l\]and \[T\] are required. Error in the measurement of which of these will have larger effect on the value of ?g? thus obtained and why? What is done to minimize this error?

Answer:

                Time period of a simple pendulum, \[T=2\pi \sqrt{\frac{l}{g}}\]          \[\therefore \]  \[g=\frac{4{{\pi }^{2}}l}{{{T}^{2}}}\] Clearly, the error in the measurement of time period T has larger effect on the value of g than the error in the measurement of length \[l\]. Reasons (i) T is very small. (ii) In contrast to \[l,={{T}^{2}}\] appears in the formula for g. To minimise the error, time period for a large number of oscillations is measured.