Practicing Success
The period of oscillation of a simple pendulum is given by T=2$\pi√(\frac{l}{g})$ here l is about 100 cm and is known to have 1mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is |
0.1% 1% 0.2% 0.8% |
0.2% |
T=2$\pi√(\frac{l}{g})$ $T^2=\frac{4\pi^2l}{g}$ $\Rightarrow g = \frac{4\pi^2 l}{T^2}$ $\Rightarrow \frac{\Delta g}{g} = \frac{\Delta l}{l} + 2\frac{\Delta T}{T}$ Error in l = $\frac{0.1cm}{100cm}\times100$%=0.1% Error in T = $\frac{0.1cm}{2\times100cm}\times100$%=0.05% % Error in g = % Error in l + 2$\times$ % Error in T = 0.1% + 2$\times$ 0.05% = 0.2%
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