First slide

Thermal expansion

Question

The diameter of a metal ring is $' D'$ and coefficient of linear expansion is $α$ , if the temperature of the ring is increases by $1^{0} C$ , The circumference of the ring will increase by $x π D α$ where $x =$

Moderate

A

1
B

2
C

3
D

4

Solution

$c i r c u m f e r e n c e o f r i n g i s S = 2 π R = 2 π \frac{D}{2} S = π D d i f f e r e n t i a t e Δ S = π Δ D c o e f f i c i e n t o f l i n e a r e x p a n s i o n α = \frac{Δ D}{D Δ t} \Rightarrow Δ D = D α Δ t; Δ S = x π D α; s u b s t i t u t e i n a b o v e e q u a t i o n x π D α = π D α Δ t x = Δ t g i v e n Δ t =1 \Rightarrow x = 1$

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