A clock with an iron pendulum keeps correct time at `15^(@)C`. If th room temperature rises to `20^(@)C` , the error in second per day will be (coefficient of linear expansion of iron is `0.000012^(@)C`)

Options

A. 2.5 s
B. 2.6 s
C. 2.4 s
D. 2.2 s

Answer

B

Explanation

Time period,` ' T' = 2pi sqrt((l)/(g))`
`(Delta T)/(T) = (1)/(2) (Delta l)/(l)`
`(Delta l)/(l) = (2 Delta T)/(T)`
Coefficient of linear expansion ,
`alpha = (Delta l)/(l Delta t)`
`implies (Delta l )/ (l) = alpha Delta t `
`implies (2 Delta T)/(t) = alpha Delta t`
`implies (2 Delta t)/(T) = 0.000012 xx (20-15)`
`implies delta T = (0.000012 xx 5 xx (24 xx 60xx 60))/(2)`
`therefore delta T = 2.6 s`