Errors in measurementEasy
Question
A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with least count of 1 s for this and records 40 s for 20 oscillations. For this observation, which of the following statement(s) is/are true?
Options
A.Error ᐃT in measuring T, the period, is 0.05 s
B.Error ᐃT in measuring T, the period, is 1 s
C.Percentage error in determination of g 5 %
D.Percentage error in determination of g 2.5 %
Solution
T = 
= 2s
Further, t = nT = 20 T or ᐃt = 20 ᐃT
∴
or ᐃT =
ᐃT = 
(1) = 0.05 s
Further, T = 2π
or T ∝ g-1/2 
× 100 = - 
× 
× 100
or % error in determination of g is
× 100 = - 200 × 
= - 
= - 5%
∴ correct options are (a) and (c).
= 2sFurther, t = nT = 20 T or ᐃt = 20 ᐃT
∴
or ᐃT =
ᐃT = (1) = 0.05 sFurther, T = 2π
or T ∝ g-1/2 × 100 = - × × 100or % error in determination of g is
× 100 = - 200 × = - = - 5%∴ correct options are (a) and (c).
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