A pendulum clock having copper rod keeps correct time at `20^@ C`. It gains 15 seconds per day if cooled to `0^@C`. Calculate the coefficient of linear expansion of copper.

Options

A. `1.7xx10^(-4)//^@C`
B. `1.7xx10^(-5)//^@C`
C. `3.4xx10^(-4)//^@C`
D. `3.4xx10^(-5)//^@C`

Answer

B

Explanation

`(T_(20)-T_0)/(T_0)=(1)/(2)xxalphaxx20=10alpha`
Here `T_(20)` is the correct time period.The time period at `0^@C` is smaller so that the clock runs fast. The time gained in 24 h.
`=24hxxalphaxx10`
`implies15s=24hxxalphaxx10`
`alpha=(15s)/(86400sxx10^@C)=1.7xx 10^(-5)^(@)//C`