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Question

A rod is measured to be of length 50 cm at 10C. Its length measured at 50C is x. Find x, if thermal coefficient of linear expansion of the rod is 2×105/C and of the scale is 3×105/C.

A
49.98 cm
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B
49.99 cm
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C
50.01 cm
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D
50.02 cm
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Solution

The correct option is A 49.98 cm
Here L0=50 cm
α0=2×105/C [of rod]
αs=3×105/C [of scale]
T0=10C
T=50C
Using formula,
Measured length of rod at temperature T is :
x=L0[1+(α0αs)(TT0)]
x=50[1+(2×1053×105)(5010)]
x=50[1+(105)(40)]
x=50[14×104]
x=50[10.0004]
x=50(0.9996)
x=49.98 cm

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