Answer to Question #75499 in Mechanics | Relativity for Vaibhavi

Question

A simple pendulum may be used to determine a value for the acceleration of free fall g. Measurements are made of the length L of the pendulum and the period T of oscillation. The values obtained, with their uncertainties are shown as

T=(1.93+_0.03)s
L=(92+_1)cm
(its a plus and under is a minus)

a) calculate the percentage uncertainty in the measurement
i) the period T
ii) the length L

b) The relationship between T, L and g is given by

g= 4 Pi^2 (symbol of Pi) L/ T^2

Using your answer in (a), calculate the percentage uncertainty in the value of g

c) The values of L and the T are used to calculate a value of g as 9.751 ms^-2

i) by reference to the measurements of L and T, suggest why it would not be correct to quote the value of g as 9.751ms^-2

ii) Use your answer in (b) to determine the absolute uncertainty in g.
Hence state the value of g, with its uncertainty, to an appropriate number of significant figures.