The coefficient of linear expansion varies linearly from `alpha_(1)` and `alpha_(2)` in a rod of length `l`. Find the increase in length when its temperature is increased by `DeltaT`.

Options

A. `((alpha_(1)+alpha_(2))/(2))lDeltaT`
B. `(alpha_(1)+alpha_(2))lDeltaT`
C. `(alpha_(1)+(alpha_(2))/(2))lDeltaT`
D. `((alpha_(1))/(2)+alpha_(2))lDeltaT`

Answer

A

Explanation

Time lost or time gained by pendulum clock per second is given by `Deltat=(1)/(2)alphaDeltaT`
implies time lost or gained per day is `Deltat=((1)/(2)alphaDeltaT)xx86400`
If graduation temperature of clock is `T_(0)` at `15^(@)C`, clock is gaining 5 sec.
`implies 5=(1)/(2)alpha(T_(0)-15)xx86400implies2(T_(0)-15)=(30-T_(0))implies T_(0)=20^(@)C`
`5=(1)/(2)alpha(20-15)86400`
`alpha=(2)/(86400)implies alpha=2.3 xx10^(-5)//.^(@)C`