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Question

A barometer reads 75.0 cm on a steel scale. The room temperature is 30C. The scale is correctly graduated for 0C. The coefficient of linear expansion of steel is α = 1.2 × 105/C and the coefficient of volume expansion of mercury is γ = 1.8 × 104/C. Find the correct atmospheric pressure.


A

75 cm

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B

74.89 cm

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C

74.35 cm

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D

75.35 cm

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Solution

The correct option is B

74.89 cm


The 75 cm length of steel at 0C will become lθ at 30C where,

Iθ = (75cm)[1+α(30C)]. ................(1)

The length of mercury column at 30C is lθ. Suppose the length of the mercury column, if it were at 0C, is l0. Then,

Iθ = I0[1+γ3(30C)]. ................(2)

By (1) and (2),

I0[1+γ3(30C)] = 75cm[1+(30C)]

Or, I0 = 75cm [1+α(30C)][1+γ3(30C)]

= 75 cm [1+(αγ3)(30C)]

= 74.89 cm.


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