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Question

The radius of curvature of a concave mirror measured by a spherometer is given by R=l26h+h2. The measured value of l is 3cm using a meter scale with least count 0.1cm and measured value of h is 0.045cm using spherometer with least count 0.005cm. Compute the relative error in measurement of radius of curvature.


A
3
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B
0.3
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C
0.2
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D
0.6
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Solution

The correct option is A 0.3
Given, l=3cm,Δl=0.1cm,h=0.045cm,Δh=0.005cm
Now, R=l26h+h2
Take ln and differentiate (only be taken magnitude)
so, relative error , ΔRR=2Δll+Δhh+Δhh=20.13+20.0050.045=0.3

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