A clock with a brass pendulum shaft keeps correct time at a certain temperature.
a. How closely must the temperature be controlled if the clock is not to gain or lose more that 1 s a day? Does the answer depend on the period of the pendulum?
b. Will an increase of temperature cause the clock to gain or lose? `(alpha_("brass")=2 xx 10^(-5)//^(@)C)`

Explanation

a. Number of seconds lost or gained per day`=(1)/(2)alphathetaxx86400`,
where `theta=`rise or drop in temperature, `alpha=` coeff. Of linear expansion of shaft.
we want that `|(1)/(2)alphathetaxx86400|lt1`
`implies |theta|lt(2)/(2xx10^-5xx86400)implies|theta|lt1.1574.^@C`
Hence temperature should not increase or decrease by more that `1.1574.^@C`. It does not depend upon time period.
b. An increase in temperature makes the pendulum slow and hence clock loses time.