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Question

The coefficient of volumetric expansion of mercury is 8×105C. A thermometer bulb has a volume 106m3 and cross section of stem is 0.004cm2. Assuming that bulb is filled with mercury at 0C, then the length of the mercury column at 100C is:


A

18.8 mm

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B

9.2 mm

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C

7.4 cm

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D

4.5 cm

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Solution

The correct option is D

4.5 cm


The volumetric expansion can be written as,
V2=V1(1+γΔθ)
where, V2 is the final volume, V1 is the initial volume, γ is the coefficient of volumetric expansion and Δθ is the change in temperature.
or, Change in volume,V2V1=V1γΔθ
As we know, Change in volume=Area×Change in length
or, V2V1=Area×Change in length
or, Change in length=V2V1Area
or, Change in length=V1γΔθA
Given, V1=106 m3, A=0.004 cm2=0.004×104 m2, γ=8×105 C,
Δθ=1000=100C
Therefore,
Change in length=106×8×105×1000.004×104
or, Change in length=2×102m=2cm


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