A clock pendulum made of invar has a period of `0.5sec` at `20^(@)C`. If the clock is used in a climate where the temperature average to `30^(@)C`, how much time does the clock loose in each oscilliation. For innar `alpha = 9 xx 10^(-7) ^(@)C^(-1)`

Options

A. `2.25 xx 10^(-6)s`
B. `2.5 xx 10^(-7)s`
C. `5 xx 10^(-7)s`
D. `1.125 xx 10^(-6)s`

Answer

A

Explanation

Time period of simple pendulum,
`T=2pi sqrt((l)/(g))rArr (Delta T)/(T)=(1)/(2)(Delta l)/(l)`
But at temperature `theta^(0)`C, increase in length of pendulum,
`(Delta l)/(l)=alpha Delta theta`
`therefore" "(Delta T)/(T)=(1)/(2)alpha Delta theta`
or `(Delta T)/(T)=(1)/(2)xx 9 xx 10^(-7) xx (30-20)`
`= (1)/(2) xx 9 xx 10^(-7) xx 10 = 4.5 xx 10^(-6)`
or `Delta T = 4.5 xx 10^(-6) xx 0.5 = 2.25 xx 10^(-6)s`