Question

A wire of length 60 cm is bent into a circle
with a gap of 1 cm at its ends. On heating i
by 100°C, the length of the gap increases to
1.02 cm. a. of material of wire is
1) 2 x 10-41°C 2) 4 x 10-41°C
3) 6 x 10-4°C 4 ) 1 X 1041°C


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Answer 1

answer : 2 × 10^-4 /°C

explanation : a wire is bent into a circle with gap of 1cm at its ends. o. heating by 100°C , the length of gap increases to 1.02cm .

using formula, $l=l_0[1+\alpha\Delta T]$

here, $l_0$ = 1cm , ∆T = 100°C and l = 1.02 cm

so, 1.02cm = 1cm[1 + α × 100]

or, 1.02 = 1 + α × 100

or, 0.02 = α × 100

or, α = 2 × 10^-4/°C

hence, coefficient of linear expansion of material is 2 × 10^-4/°C

Answer 2

Answer:

Since on heating the length of the wire increases, it expands outwards, making the size of the ring bigger. consequently, the gap in the ring also becomes bigger in the same proportion.

So, if 1 cm become 1.02 cm, 60 cm will become 61.2 cm

So, change in length =61.2 cm −60 cm = 1.2 cm

original length is 60 cm and change in temperature = 1000 C

Putting these values in the formula of α=l×dtdl, where dl=  Change in length and dt= change in temperature,

We get, α=2×10−4/∘ C

Hope this would help you guys

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