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(C) By the principle of conservation of energy,the initial potential energy of the charge distribution is converted into kinetic energy as it expands.

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Vedclass · Answer

(C) By the principle of conservation of energy,the initial potential energy of the charge distribution is converted into kinetic energy as it expands.The initial potential energy of a spherical shell of charge $Q$ and radius $R_0$ is $U_i = \frac{k Q^2}{2 R_0}$.At any instantaneous radius $R(t)$,the potential energy is $U_t = \frac{k Q^2}{2 R(t)}$ and the kinetic energy is $K_t = \frac{1}{2} m v^2$.Since the system starts from rest,$K_i = 0$. Thus,$U_i = U_t + K_t$.$\frac{k Q^2}{2 R_0} = \frac{k Q^2}{2 R(t)} + \frac{1}{2} m v^2$$\frac{1}{2} m v^2 = \frac{k Q^2}{2} \left( \frac{1}{R_0} - \frac{1}{R(t)} ight)$$v = \sqrt{\frac{k Q^2}{m} \left( \frac{1}{R_0} - \frac{1}{R(t)} ight)}$As $R(t) 	o R_0$,$v 	o 0$. As $R(t) 	o \infty$,$v 	o \sqrt{\frac{k Q^2}{m R_0}}$,which is a constant value. The function $v(R)$ starts at $0$ and increases,approaching a horizontal asymptote. This behavior is best represented by Graph $C$.

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