A clock which keeps correct time at $25^{o} C$ has a pendulum made of a metal. The temperature falls to $0^{o} C$ . If the coefficient of linear expansion of the metal is 1.9 x $10^{- 5}$ per $^{o} C$ , then number of second the clock gains per day is:

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Solution

The gain or loss in the time w.r.t. change in temperature is given by
$△ t = \frac{1}{2} α △ θ t$
Now, In this question, $△ θ = - 25^{o} C α = 1.9 \times 10^{- 5} t = 24 \times 60 \times 60 s$
So, putting values in the equation
$△ t = \frac{1}{2} \times 1.9 \times 10^{- 5} \times (- 25) \times 24 \times 60 \times 60 △ t = - 20.520 s$
Negative sign shows that the clock will loose $20.52 s$ per day.

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A clock which keeps correct time at 25oC has a pendulum made of a metal. The temperature falls to 0oC. If the coefficient of linear expansion of the metal is 1.9 x 10−5 peroC, then number of second the clock gains per day is:

The gain or loss in the time w.r.t. change in temperature is given by△t=12α△θtNow, In this question, △θ=−25oCα=1.9×10−5t=24×60×60sSo, putting values in the equation△t=12×1.9×10−5×(−25)×24×60×60△t=−20.520sNegative sign shows that the clock will loose 20.52s per day.

A clock which keeps correct time at $25^{o} C$ has a pendulum made of a metal. The temperature falls to $0^{o} C$ . If the coefficient of linear expansion of the metal is 1.9 x $10^{- 5}$ per $^{o} C$ , then number of second the clock gains per day is: