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(C) The formula for acceleration due to gravity is $g = \frac{4\pi^2 L}{T^2}$.Taking the relative error, we have $\frac{\Delta g}{g} = \frac{\Delta L}

Vedclass · Accepted Answer

$6.8$

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(C) The formula for acceleration due to gravity is $g = \frac{4\pi^2 L}{T^2}$.Taking the relative error, we have $\frac{\Delta g}{g} = \frac{\Delta L}{L} + 2\frac{\Delta T}{T}$.Given:$L = 55.0\,cm$, $\Delta L = 1\,mm = 0.1\,cm$.Time for $20$ oscillations is $t = 30\,s$, so $T = \frac{30}{20} = 1.5\,s$.The least count of the watch is $1\,s$, so the error in total time is $\Delta t = 1\,s$. Thus, $\Delta T = \frac{\Delta t}{20} = \frac{1}{20} = 0.05\,s$.Now, calculate the percentage error:$\frac{\Delta g}{g} 	imes 100 = \left( \frac{\Delta L}{L} + 2\frac{\Delta T}{T} ight) 	imes 100\%$$= \left( \frac{0.1}{55.0} + 2 	imes \frac{0.05}{1.5} ight) 	imes 100\%$$= \left( 0.001818 + 0.06666 ight) 	imes 100\%$$= 0.06848 	imes 100\% \approx 6.8\%$.

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