First slide

Thermal expansion

Question

Write the expression for variation in time period of a pendulum clock due to thermal expansion

Moderate

A

$\frac{Δ T}{T} = \frac{1}{2} α Δ t$
B

$Δ T = \frac{1}{2} \frac{α}{T} Δ t$
C

$T = \frac{1}{2} α Δ t$
D

None

Solution

$t i m e p e r i o d o f s i m p l e p e n d u l u m i s T = 2 π \sqrt{\frac{l}{g}} h e r e l i s l e n g t h o f t h e p e n d u l u m, g i s a c c e l e r a t i o n d u e t o g r a v i t y \Rightarrow T α \sqrt{l} d i f f e r e n t i a t e a b o v e e q u a t i o n \frac{Δ T}{T} = \frac{1}{2} \frac{Δ l}{l} - - - (1) a s c o e f f i c i e n t o f l i n e a r e x p a n s i o n i s α = \frac{Δ l}{l Δ t e m p e r a t u r e} \Rightarrow α Δ t = \frac{Δ l}{l} - - - (2) s u b s t i t u t e e q n (2) i n e q n (1) \frac{Δ T}{T} = \frac{1}{2} α Δ t$

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