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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    Infinite number of masses, each 1 kg, are placed along the x-axis at\[x=\pm \text{ }1\text{ }m,\pm 2m,\pm \text{ }4\] \[m,\pm \text{ }8\text{ }m,\pm \text{ }16m....\]The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin\[(x=0)\]is

    A)  \[G/2\]               

    B)         \[G\]                   

    C)  \[2G\]                 

    D)         \[4G\]

    E)  \[8G\]

    Correct Answer: C

    Solution :

    Gravitational potential \[V=GM\left( \frac{1}{{{r}_{1}}}+\frac{1}{{{r}_{2}}}+\frac{1}{{{r}_{3}}}+...... \right)\] \[=G\times 1\left( \frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+.... \right)\] \[=G\left( \frac{1}{1-1/2} \right)\]   \[\left( \because sum\,of\,GP=\frac{a}{1-r} \right)\]


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