The period of oscillation of a simple pendulum is given by \(T = 2 \pi \sqrt{\frac{l}{g}}\) where l is about 100 cm and is known to have 1 mm accuracy. The period is about 2 s . The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is
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\(T = 2 \pi \sqrt{l/g}\) \(\Rightarrow T^{2} = \frac{4 \pi^{2} l}{g}\) \(\Rightarrow g = \frac{4 \pi^{2} l}{T^{2}}\)
Here % error in l = \(\frac{1\,\text{mm}}{100\,\text{cm}} \times 100 = \frac{0.1}{100} \times 100 = 0.1\%\) and % error in T = \(\frac{0.1}{2 \times 100} \times 100 = 0.05\%\)
∴ ∴ % error in g = % error in l + 2(% error in T )
\(= 0.1 + 2 \times 0.03\) = 0.2 %
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