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JEE Main & Advanced JEE Main Paper (Held on 08-4-2019 Afternoon)

  • question_answer
    A positive point charge is released from rest at a distance\[{{r}_{0}}\]from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :-                                          [JEE Main 8-4-2019 Afternoon]

    A) \[\text{v}\propto {{\text{e}}^{+r/{{r}_{0}}}}\]               

    B) \[\text{v}\propto \ell n\left( \frac{r}{{{r}_{0}}} \right)\]

    C) \[\text{v}\propto \left( \frac{r}{{{r}_{0}}} \right)\]   

    D)   \[\text{v}\propto \sqrt{\ell n\left( \frac{r}{{{r}_{0}}} \right)}\]

    Correct Answer: D

    Solution :

    \[\frac{1}{2}m{{V}^{2}}=-q({{V}_{f}}-{{V}_{i}})\]           \[E=\frac{\lambda }{2\pi {{\varepsilon }_{0}}r}\]           \[\Delta V=\frac{\lambda }{2\pi {{\varepsilon }_{0}}}\ell n\left( \frac{{{r}_{0}}}{r} \right)\]           \[\frac{1}{2}m{{v}^{2}}=\frac{-q\lambda }{2\pi {{\varepsilon }_{0}}}\ell n\left( \frac{{{r}_{0}}}{r} \right)\]           \[\text{v}\propto \sqrt{\ell n\left( \frac{r}{{{r}_{0}}} \right)}\]


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