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

Options

A. a)0.08
B. b)0.03
C. c)0.04
D. d)0.05

Answer

D

Explanation

The period of simple pendulum is
`T=2pi sqrt(l/g)`
or `(Delta T)/T=1/2((Deltal)/l-(Deltag)/g)`
or `(Delta g)/g= (Delta l)/l-(2 Delta l)/T`
`therefore` Maximum percentage error in g,
`(Delta g)/g times 100= (Delta l)/l times 100+ (2 Delta T)/T times 100`
`=1+2 times 2`
`=5%`