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#5 | Error Analysis : Propagation of Error (Division) & Example

(Physics) > Units and Measurement

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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

(1) 0.1%

(2) 1%

(3) 0.2%

(4) 0.8%

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The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed

(1) 11%

(2) 8%

(3) 5%

(4) 1%

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The random error in the arithmetic mean of 100 observations is *x*; then random error in the arithmetic mean of 400 observations would be

(1) 4*x*

(2) $\frac{1}{4}x$

(3) 2*x*

(4) $\frac{1}{2}x$

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Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is

(1) 1%

(2) 3%

(3) 5%

(4) 7%

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The mean time period of *second*'s pendulum is 2.00*s* and mean absolute error in the time period is 0.05*s*. To express maximum estimate of error, the time period should be written as

(1) (2.00 ± 0.01) *s*

(2) (2.00 + 0.025) *s *

(3) (2.00 ± 0.05) *s*

(4) (2.00 ± 0.10) *s*

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