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Q.

A bullet of mass m and charge q is fired towards a solid uniformly charged sphere of radius R and total charge+ q. If it strikes the surface of sphere with speed u, find the minimum speed u so that it can penetrate through the sphere. (Neglect all resistive forces or friction acting on bullet except electrostatic forces)

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a

$\frac{q}{\sqrt{2 {πε}_{0} mR}}$

b

$\frac{\sqrt{3} q}{\sqrt{4 {πε}_{0} mR}}$

c

$\frac{q}{\sqrt{8 {πε}_{0} mR}}$

d

$\frac{q}{\sqrt{4 {πε}_{0} mR}}$

answer is B.

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Detailed Solution

$(TE)_{surface} = (PE)_{centre}$
Velocity at centre is nearly zero then it can cross the sphere
$\begin{array}{l} \frac{1}{4 {πε}_{0}} \frac{q \cdot q}{R} + \frac{1}{2} {mv}^{2} = \frac{3}{2} (\frac{1}{4 {πε}_{0}} \frac{q}{R}) q \\ \Rightarrow v = \frac{q}{\sqrt{4 {πε}_{0} mR}} \end{array}$

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