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Question:

There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is?

Solution:

At any instant 't'
Total energy of charge distribution is constant
i.e. 1/2mV² + KQ²/2R = 0 + KQ²/2R0
∴1/2mV² = KQ²/2R0 - KQ²/2R
∴V = √[KQ²/m(1/R0 - 1/R)] = C√(1/R0 - 1/R)
Also the slop of v-s curve will go on decreasing
∴Graph is correctly shown by option (1)