Question

The radius of curvature of a concave mirror measured by a spherometer is given by $R=\frac{l^2}{6h}+\frac{h}{2}$. 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. $3$
• B. $0.3$
• C. $0.2$
• D. $0.6$

Answer 1

Answer: (B)

$0.3$

Given, $l=3cm,\Delta l=0.1cm,h=0.045cm,\Delta h=0.005cm$
Now, $R=\frac{l^2}{6h}+\frac{h}{2}$

Take $ln$ and differentiate (only be taken magnitude)
so, relative error , $\frac{\Delta R}{R}=2\frac{\Delta l}{l}+\frac{\Delta h}{h}+\frac{\Delta h}{h}=2\frac{0.1}{3}+2\frac{0.005}{0.045}=0.3$