An electron revolves in a circular orbit of radius r completely inside a positively charged solid non-conducting sphere of radius R ( r < R ) having a uniform volume charge density . The graph that correctly represents the variation of the kinetic energy ( KE ) of the electron as a function of the radius r is best described as :

Step-by-step solution

The electric field E at a distance r inside a uniformly charged solid sphere ( r E = r 3 ₀ The electrostatic force on the electron provides the necessary centripetal force: F_e = eE = e r 3 ₀ Equating this to the centripetal force: mv^2 r = e r 3 ₀ Multiplying both sides by r , we get: mv^2 = e r^2 3 ₀ The kinetic energy ( KE ) of the electron is: KE = 1 2 mv^2 = 1 2 ( e r^2 3 ₀ ) = e r^2 6 ₀ This shows that KE r^2 . Therefore, the graph of KE versus r is a parabola passing through the origin and opening upwards. A