A charged particle with charge $q$ and mass $m$ starts with an initial kinetic energy $K$ at the middle of a uniformly charged spherical region of total charge $Q$ and radius $R$ . $q$ and $Q$ have opposite signs. The spherically charged region is not free to move . The value of $K_0$ is such that the particle will just reach the boundary of the spherically charged region. How much time does it take for the particle to reach the boundary of the region.
A charged particle with charge $q$ and mass $m$ starts with an initial kinetic energy $K$ at the middle of a uniformly charged spherical region of total charge $Q$ and radius $R$ . $q$ and $Q$ have opposite signs. The spherically charged region is not free to move . The value of $K_0$ is such that the particle will just reach the boundary of the spherically charged region. How much time does it take for the particle to reach the boundary of the region.
- A
$t = \frac{\pi }{2}\sqrt {\frac{{4\pi { \in _0}m{R^3}}}{{qQ}}} $
- B
$t = \frac{\pi }{2}\sqrt {\frac{{2\pi { \in _0}m{R^3}}}{{qQ}}} $
- C
$t = \frac{\pi }{4}\sqrt {\frac{{2\pi { \in _0}m{R^3}}}{{qQ}}} $
- D
$t = \frac{\pi }{4}\sqrt {\frac{{4\pi { \in _0}m{R^3}}}{{qQ}}} $
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- [AIIMS 2004]