A) \[9.378\,{{m}^{2}}\]
B) \[9.37\,{{m}^{2}}\]
C) \[9.378248\,{{m}^{2}}\]
D) \[9.3782\,{{m}^{2}}\]
Correct Answer: A
Solution :
Significant figures is a method of expressing error in measurement. Significant figures follow certain set of rules. That is any zeros that are between non-zeros are also considered significant. Hence, breadth of metal b = 3.002 m has four significant figures. Also all non-zero digits are significant, \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{({{k}_{1}}+{{k}_{2}})m}}\] Length of metal =3.124m has four significant figures. Since, length and breadth have four significant figure, therefore \[\frac{1}{k}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}\] \[k=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\] \[n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}\] will also have four significant figures. Hence, area \[=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{({{k}_{1}}+{{k}_{2}})m}}\]
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