First slide

Thermal expansion

Question

pendulum clock goes slow by 10 sec/day when atmospheric temperature is 40°C and goes fast by 8 sec/day when temperature is 20°C. The temperature at which the clock gives correct time is

Moderate

A

30°C
B

29°C
C

28°C
D

27°C

Solution

The difference in time period of pendulum clock is
$Δt = \frac{1}{2} αΔθ \Rightarrow Δt \propto Δθ$
Let the clock give correct time at $θ^{o}$ C.
$\frac{40 - θ}{θ - 20} = \frac{10}{8} = \frac{5}{4} \Rightarrow 260 = 9 θ \Rightarrow θ = \frac{260}{9} = 28 {.9}^{\circ} C$

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