JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

  • question_answer
    This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: It is not possible to make a sphere of capacity 1 farad using a conducting material. Statement 2: It is possible for earth as its radius is\[6.4\times {{10}^{6}}m.\]   JEE Main Online Paper (Held On 26-May-2012)  

    A)  Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

    B)                        Statement 1 is false, Statement 2 is true.

    C) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

    D)                        Statement 1 is true, Statement 2 is false.

    Correct Answer: D

    Solution :

                    Capacitance of sphere is given by : \[C=4\pi {{\in }_{0}}r\] If, C = IF then radius of sphere needed: \[r=\frac{C}{4\pi {{\in }_{0}}}=\frac{1}{4\pi \times 8.85\times {{10}^{-12}}}\] or,\[r=\frac{{{10}^{12}}}{4\pi \times 8.85}=9\times {{10}^{9}}m\] \[9\times {{10}^{9}}m\]is very large, it is not possible to obtain such a large sphere. In fact earth has radius \[6.4\times {{10}^{6}}m\]only and capacitance of earth is\[711\mu F.\]


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