A) \[(14.3\,\pm \,0.1)\,cm\]
B) \[(14.3\,\pm \,0.5)\,cm\]
C) \[(30.1\,\pm \,0.1)\,cm\]
D) \[(25.3\,\pm \,0.5)\,cm\]
Correct Answer: A
Solution :
We have \[=\frac{1}{f}=\frac{1}{u}+\frac{1}{v}=\frac{v+u}{uv}\] \[\therefore \] \[f=\frac{uv}{v+u}\] \[=\frac{(50.1)(20.1)}{(50.1+20.1)}\] \[=14.3\,cm\] From \[\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\] \[\frac{-\Delta t}{{{f}^{2}}}=\frac{-\Delta u}{{{u}^{2}}}+\frac{-\Delta v}{{{v}^{2}}}\] \[\Rightarrow \] \[\Delta f=\Delta u{{\left( \frac{f}{u} \right)}^{2}}+\Delta v{{\left( \frac{f}{u} \right)}^{2}}\] \[=0.5{{\left( \frac{14.3}{50.1} \right)}^{2}}+0.2{{\left( \frac{14.3}{20.1} \right)}^{2}}\] \[=0.04+0.10\] \[=0.14\,cm\] \[\therefore \] \[f=(14.3\pm 0.1)\,cm\]
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