The coefficient of linear expansion varies linearly from `alpha_(1)` to `alpha_(2)` in a rod of length l. Find the increase in length when the tempera

Question

The coefficient of linear expansion varies linearly from `alpha_(1)` to `alpha_(2)` in a rod of length l. Find the increase in length when the tempera

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

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - A
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`