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Hi
Consider the force that acts on the charge wen it is inside the tunnnel . the force is Kqr/R3 .
Therefore by integrating This force with respect to r, from R to 0, then we can calculate the work done in bringing the charge q from R to 0.
This work done is responsible for change in kinetic energy of the charge,. Hence, 1/2m(vfinal2- v2)= work done, hence we can find v at the centre of the sphere.
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