In an experiment to determine the acceleration due to gravity

PHYSICS · Single correct · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

g

, the formula used for the time period of a periodic motion is

T = 2\pi\sqrt{\frac{7(R-r)}{5g}}

. The values of

R

and

r

are measured to be

(60 \pm 1)

mm and

(10 \pm 1)

mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is (are) true? [Adv. 2016] (1) The error in the measurement of

r

is 10% (2) The error in the measurement of

T

is 3.75% (3) The error in the measurement of

T

is 2% (4) The error in the determined value of

g

is 11%

Related theory

Measurement Errors
Errors in measurement
Arithmetic operations and uncertainty propagation

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