The percentage errors in the measurement of length and time period of a simple pendulum are 1% and 2% respectively. Then, the maximum error in the measurement of acceleration due to gravity is

Options

A. 0.08
B. 0.03
C. 0.04
D. 0.05

Answer

D

Explanation

Time period of simple pendulum is
`T=2pisqrt((l)/(g))` or `(DeltaT)/(T)==(1)/(2)((Deltal)/(l)-(Deltag)/(g))`
`implies(Deltag)/(g)=(Deltal)/(l)-(2DeltaT)/(l)`
`therefore` Maximum percentage error in g,
`(Deltag)/(g)xx100=(Deltal)/(l)xx100+(2DeltaT)/(T)xx100`
`=1xx100+2xx2xx100=5xx100=5%`