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

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(C) The formula for acceleration due to gravity is $g = 4\pi^2 \left(\frac{l}{T^2}ight)$.Taking the relative error,we get $\frac{\Delta g}{g} = \frac{\Delta l}{l} + 2\frac{\Delta T}{T}$.Given that the percentage error in length $\left(\frac{\Delta l}{l} 	imes 100ight) = 1\%$ and the percentage error in time period $\left(\frac{\Delta T}{T} 	imes 100ight) = 3\%$.Since errors are always additive,the percentage error in $g$ is $\frac{\Delta g}{g} 	imes 100 = \left(\frac{\Delta l}{l} 	imes 100ight) + 2 	imes \left(\frac{\Delta T}{T} 	imes 100ight)$.Substituting the values: $\frac{\Delta g}{g} 	imes 100 = 1\% + 2(3\%) = 1\% + 6\% = 7\%$.Therefore,the percentage error in the measurement of $g$ is $7\%$.

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