A rod is measured to be of length 50cm at 10∘C. Its length measured at 50∘C is x. Find x, if thermal coefficient of linear expansion of the rod is 2×10−5/∘C and of the scale is 3×10−5/∘C.
A
49.98cm
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B
49.99cm
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C
50.01cm
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D
50.02cm
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Solution
The correct option is A49.98cm Here L0=50cm α0=2×10−5/∘C [of rod] αs=3×10−5/∘C [of scale] T0=10∘C T=50∘C
Using formula,
Measured length of rod at temperature T is : x=L0[1+(α0−αs)(T−T0)] x=50[1+(2×10−5−3×10−5)(50−10)] x=50[1+(−10−5)(40)] x=50[1−4×10−4] x=50[1−0.0004] x=50(0.9996) ∴x=49.98cm