A pendulum clock keeps correct time at 0,^oC . thermal coefficient of linear expansion of material o

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10-1.Thermometry, Thermal Expansion and Calorimetry

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A pendulum clock keeps correct time at $0\,^oC$. The thermal coefficient of linear expansion of the material of the pendulum is $\alpha $. If the temperature rises to $t\,^oC$, then the clock loses per day by (in second)

A

$\alpha t$

B

$\frac{1}{2}\alpha t$

C

$\alpha t \times 86400$

D

$\frac{1}{2}\alpha t \times 86400$

Solution

Time loss or gain is given by,

$\Delta t=\left(\frac{\Delta T}{T}\right) t=\frac{1}{2} \alpha t$

This is time lost per second.

Since, there are $24 \,hr$ in a day

$24 \times 3600=86400$ per day.

Time loss per day $A t=\frac{1}{2} \alpha t \times 86400$

Standard 11

Physics

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