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JEE Main & Advanced Sample Paper JEE Main Sample Paper-34

  • question_answer
    If infinite number of particle each of mass m are placed on x-axis at x = r, x = 2r, x = 4r..... and so on then magnitude of net gravitational field intensity at the origin will be:

    A)  \[\frac{5GM}{4{{r}^{2}}}\]                         

    B)  \[\frac{4GM}{3{{r}^{2}}}\]

    C)  \[\frac{3GM}{2{{r}^{2}}}\]                         

    D)  \[\frac{2GM}{{{r}^{2}}}\]

    Correct Answer: B

    Solution :

    \[{{E}_{g}}=+\,\frac{Gm}{{{r}^{2}}}\,+\frac{Gm}{{{(2r)}^{2}}}..............\infty \]             \[=+\,\frac{Gm}{{{r}^{2}}}\,+(1+\frac{1}{4}\,+\frac{1}{16}\,+...........\infty )\]             \[=+\,\frac{Gm}{{{r}^{2}}}\,+\left[ \frac{1}{1-\frac{1}{4}} \right]\,=\frac{4Gm}{3{{r}^{2}}}\]


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