In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is T = 2π (7(R - r))/(5g) . The values of R and r are measured to be (60 ± 1)mmand(10 ± 1)mm

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Correct answer: A. The error in the measurement of r is 10%.

T Absolute error 1 0.52 - 0.04 2 0.56 00 3 0.57 + 0.01 4 0.54 - 0.02 5 0.59 + 0.03 T _ avg = 0.556 = 0.56 Avg. absolute error (0 . 04 + 0 + 0 . 01 + 0 . 02 + 0 . 03)/(5) = 0 . 02 Percentage error in time period = (∆ T)/(T) × 100% = (0 . 02)/(0 . 56) × 100% 3.57% Percentage error in radius = (∆ r)/(r) × 100% = (1)/(10) × 100 = 10% Also, g = 28π(R - r) 5 T ^ 2 Percentage error in g ,= (∆ g)/(g) = (∆ R + ∆ r)/(R - r) + (2 ∆ T)/(T) (∆ g)/(g) × 100% = (1 + 1)/(50) × 100% + 2(3.57)% 11%

In an experiment to determine the acceleration due to gravity g,...

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	T	Absolute error
1	0.52	$- 0.04$
2	0.56	00
3	0.57	$+ 0.01$
4	0.54	$- 0.02$
5	0.59	$+ 0.03$
	${T}_{avg} = 0.556$ $= 0.56$